Given that $n = 1279033001$ is a product $n = pq$ of distinct primes $p$ and $q$ and that $175205^2 ≡ 1$(mod n), factorise $n$.

Question

I have tried using Fermats factorisation and Pollard $p-$method but unfortunately I'm running into rounding errors with my calculator. I'm not sure how $175205^2 ≡ 1$(mod n) is helpful

Answer 1

We have, using $a^2-1=(a+1)(a-1)$, $$ 175205^2-1=175204\cdot 175206=(2^2\cdot 43801)\cdot (2\cdot 3\cdot 29201), $$ hence $n=29201\cdot 43801$.