Problem

(a) Prove that if d | n, then 2d − 1 | 2n − 1.[Hint: Use the identityxk − 1 = (x − 1)(xk−1...

(a) Prove that if d | n, then 2d − 1 | 2n − 1.

[Hint: Use the identity

xk − 1 = (x − 1)(xk−1 + xk−2 + ⋯ + x + 1).]


(b) Verify that 235 − 1 is divisible by 31 and 127.

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Solutions For Problems in Chapter 2.3