Math 40520 Number Theory, Evens Worksheet Page 2
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HOMEWORK 3, MATH 40520, NUMBER THEORY, EVENS.
Extra Credit: Prove that if y is a real number, and N be the collection of positive integers k
such that if p is a prime factor of k, then p ≤ y. Prove that
1
1
2
(1 + p
+ p
+ . . . ) =
.
k
p≤y
k∈N
Note that both sides involve infinite sums, so you should check convergence.
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