If p is prime > 2 then there is a easy way to solve 32n+3 = 0 mod p(adsbygoogle = window.adsbygoogle || []).push({});

if p = 1 mod 8 then m = (p-1)/4 and n = m(m+1)/2 mod p

if p = 3 mod 8 then m = (p-3)/4 and n = m(m+1)/2 mod p

if p = 5 mod 8 then m = (p-5)/8*2 + 1 and n = m(m+1)/2 mod p

if p = 7 mod 8 then m = (p-7)/8*2 + 1 and n = m(m+1)/2 mod p

Strange how triangular numbers relate to primes!

Can anyone give a proof for this relation?

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# 32n + 3 = 0 mod p formula for n

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