Suppose that we’re given the function , find the ordinary generating function associated with it in the form of . Furthermore, find/compute .

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## Posts Tagged ‘ number theory ’

15 August

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Article, Math Problems

# Power Reduction in Congruences

Suppose you have integers a,b that are relatively prime to m such that

then

14 August

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Article, Math Problems

# Even Pascals

Let , where k is an integer. Prove that for any positive integer n the number

is divisible by .

13 August

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Article, Math Problems

# Polynomial Divisors

Let . Show that for any positive integers there exists unique numbers such that the polynomial is divisible by p(x)

12 August

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Article, Math Problems

# Odd Coprimes

Let a be an odd integer. Prove that and are relatively prime for all distinct positive integers n and m.

11 August

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Article, Math Problems

# Prime Congruence Class

Show that there are infinitely many primes of the form `4k - 1`

.

10 August

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Article, Math Problems

# Sum of Divisors

Suppose we define the function as the sum of the divisors of n

Express in terms of ‘s prime factorization

9 August

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Article, Math Problems

# That Other Little Gauss Story

Determine the product of distinct positive integer divisors of .