What is the largest prime factor of 5^8 +2^2 ?
5^8 + 2^2
= 25^4 + 2^2
= 625^2 + 2^2
= (625 + 2)^2 - 2(2)(625)
= 627^2 - (2(25))^2 . a difference of squares
= 627^2 - 50^2
= (627 + 50)(627-50)
= 677(577)
both of these are primes, so the largest prime factor is 677
check:
5^8 + 2^2 = 390629 and 390629/677 = 577