What is the greatest prim factor of (4)^17-(2)^28?

[nk2120]

Anybody? Thanks!

[Misha]

What is the greatest prim factor of (4)^17-(2)^28?

First, simplify to obtain common factors:
4^17 = (2^2)^17 = 2^34

Thus question becomes:
2^34 - 2^28 = 2^28 (2^6 - 1) = 2^28 (64-1) = 2^28 (63) = 2^28 (9*7) = 2^28 (3*3*7)

Looks like 2, 3, 7 are the prime factors, and thus appears that 7 is the GCF-prime.

[RonPurewal]

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