71. For positive integers m and n, let gcd(m,n) denote the largest integer that is a factor of both m and n. Compute gcd(1, 155) + gcd(2, 155) + · · · + gcd(155,

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n (>)

m

(n^{m} + 1)

1 + n + n^{2} + . . . n^{225}

n > 1

m

n^{m} + 1

1 + n + n^{2} . . . . . n^{125}

Let $n > 1$ be a positive integer, then find the largest integer m such that ( $n^{m}$ + 1) divides $1 + n + n^{2}$ + ......+ $n^{127}$ .

(n^{m} + 1)

(1 + n + n^{2} + . . . . + n^{127})

(n^{m} + 1)

(1 + n + n^{2} + n^{3} + . . . + n^{127})

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