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Euclid's Lemma (For Prime Divisors)

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Explanations 1

Euclid's Lemma states that given a prime ppp and integers a,ba, ba,b, if p∣abp | abp∣ab, then p∣ap|ap∣a or p∣bp|bp∣b. Note that the "or" is inclusive, so it is also possible (bu…
By Jeffery Yu

Problems 1

Find the number of ordered pairs of positive integers (a,b)(a,b)(a,b) with a+ba+ba+b prime, 1≤a,b≤1001\leq a, b \leq 1001≤a,b≤100, and ab+1a+b\frac{ab+1}{a+b}a+bab+1 is an inte…