2009-12-18, 05:45 PM
a = 5^98+3
b = 5^99+1
b isn't divisible by 5, so gcd(a, b) = gcd(5a, b)
5a = 5^99+15
5a-b is 14, so the gcd must be a factor of 14 (1, 2, 7, or 14). Both numbers are even, so they're divisible by 2 -> gcd is divisible by 2. Now to prove that it equals 14, you have to show that they're divisible by 7.
... -shrugs-
b = 5^99+1
b isn't divisible by 5, so gcd(a, b) = gcd(5a, b)
5a = 5^99+15
5a-b is 14, so the gcd must be a factor of 14 (1, 2, 7, or 14). Both numbers are even, so they're divisible by 2 -> gcd is divisible by 2. Now to prove that it equals 14, you have to show that they're divisible by 7.
... -shrugs-