If you haven’t read everything I wrote last week, but would still like to solve an Erdös-Graham-problem or two with me, here is, basically, everything I know so far:

Let be a given natural number and be a prime smaller than . Let be the unique number smaller than such that holds for some . Let be the least common multiple of and be such that . And, at last, let and be coprime positive integers, such that, for , . Then:

1) , and are all equivalent

2) If , then does *not* divide

3) If is not a prime power, implies

4) For every fixed , there is a , for which

Btw, one of the problems is: prove or disprove that the greatest common divisor of and is equal to for infinitely many . Another one is to find the smallest (or at least a better upper bound for) , such that .

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