1.3 KiB
id | title | challengeType | forumTopicId | dashedName |
---|---|---|---|---|
5900f3ee1000cf542c50ff00 | Problem 130: Composites with prime repunit property | 5 | 301758 | problem-130-composites-with-prime-repunit-property |
--description--
A number consisting entirely of ones is called a repunit. We shall define R(k)
to be a repunit of length k
; for example, R(6) = 111111
.
Given that n
is a positive integer and GCD(n, 10) = 1
, it can be shown that there always exists a value, k
, for which R(k)
is divisible by n
, and let A(n)
be the least such value of k
; for example, A(7) = 6
and A(41) = 5
.
You are given that for all primes, p > 5
, that p − 1
is divisible by A(p)
. For example, when p = 41, A(41) = 5
, and 40 is divisible by 5.
However, there are rare composite values for which this is also true; the first five examples being 91, 259, 451, 481, and 703.
Find the sum of the first twenty-five composite values of n
for which GCD(n, 10) = 1
and n − 1
is divisible by A(n)
.
--hints--
compositeRepunit()
should return 149253
.
assert.strictEqual(compositeRepunit(), 149253);
--seed--
--seed-contents--
function compositeRepunit() {
return true;
}
compositeRepunit();
--solutions--
// solution required