This problem illustrates that if we are able to compute square roots (mod N), this can simplify factorization ofN. Suppose that we know (never mind how) that

23^351882^2(mod61063); 23^55^31898^2(mod61063).

Findaandbsuch thata^2b^2(mod61063) then find a factor of 61063 by computinggcd(61063, ab) (why do we expect that it is not equal to 1?).