* fix: clean-up Project Euler 221-240 * fix: corrections from review Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
1.4 KiB
id, title, challengeType, forumTopicId, dashedName
id | title | challengeType | forumTopicId | dashedName |
---|---|---|---|---|
5900f4521000cf542c50ff64 | Problem 229: Four Representations using Squares | 5 | 301872 | problem-229-four-representations-using-squares |
--description--
Consider the number 3600. It is very special, because
$$\begin{align} & 3600 = {48}^2 + {36}^2 \\ & 3600 = {20}^2 + {2×40}^2 \\ & 3600 = {30}^2 + {3×30}^2 \\ & 3600 = {45}^2 + {7×15}^2 \\ \end{align}$$
Similarly, we find that 88201 = {99}^2 + {280}^2 = {287}^2 + 2 × {54}^2 = {283}^2 + 3 × {52}^2 = {197}^2 + 7 × {84}^2
.
In 1747, Euler proved which numbers are representable as a sum of two squares. We are interested in the numbers n
which admit representations of all of the following four types:
$$\begin{align} & n = {a_1}^2 + {b_1}^2 \\ & n = {a_2}^2 + 2{b_2}^2 \\ & n = {a_3}^2 + 3{b_3}^2 \\ & n = {a_7}^2 + 7{b_7}^2 \\ \end{align}$$
where the a_k
and b_k
are positive integers.
There are 75373 such numbers that do not exceed {10}^7
.
How many such numbers are there that do not exceed 2 × {10}^9
?
--hints--
representationsUsingSquares()
should return 11325263
.
assert.strictEqual(representationsUsingSquares(), 11325263);
--seed--
--seed-contents--
function representationsUsingSquares() {
return true;
}
representationsUsingSquares();
--solutions--
// solution required