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								---
							 
						 
					
						
							
								
									
										
										
										
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								id: 5900f4da1000cf542c50ffec
							 
						 
					
						
							
								
									
										
										
										
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								challengeType: 5
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								title: 'Problem 365: A huge binomial coefficient'
							 
						 
					
						
							
								
									
										
										
										
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								videoUrl: ''
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								localeTitle: 'Problema 365: Un enorme coeficiente binomial'
							 
						 
					
						
							
								
									
										
										
										
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								## Description
 
							 
						 
					
						
							
								
									
										
										
										
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								< section  id = "description" >  El coeficiente binomial C (1018,109) es un número con más de 9 mil millones (9 ×   109) dígitos. < p >  Sea M (n, k, m) el coeficiente binomial C (n, k) módulo m. < / p > < p >  Calcule ∑M (1018,109, p < em > q< / em >  r) para 1000 < p < q < r < 5000 yp, q, r prime. < / p > < / section > 
							 
						 
					
						
							
								
									
										
										
										
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								## Instructions
 
							 
						 
					
						
							
								
									
										
										
										
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								< section  id = "instructions" > 
							 
						 
					
						
							
								
									
										
										
										
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								< / section > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								## Tests
 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								< section  id = 'tests' > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								```yml
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								tests:
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								  -  text: < code > euler365()</ code >  debe devolver 162619462356610300.
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								    testString: 'assert.strictEqual(euler365(), 162619462356610300, "< code > euler365()< / code >  should return 162619462356610300.");'
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								```
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								< / section > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								## Challenge Seed
 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								< section  id = 'challengeSeed' > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								< div  id = 'js-seed' > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								```js
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								function euler365() {
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								  // Good luck!
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								  return true;
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								}
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								euler365();
							 
						 
					
						
							
								
									
										
										
										
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								```
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								< / div > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								< / section > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								## Solution
 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								< section  id = 'solution' > 
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								```js
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								// solution required
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								```
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							 
							
								
									
								 
							
							
								< / section >