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SOLVED:(a) It has been conjectured that there exist infinitely many prime numbers p such that p=n^2+(n+1)^2 for some positive integer n ; for example, 5=1^2+2^2 and 13= 2^2+3^2. Find five more of these primes. (b) Another conjecture is that there are infinitely many prime numbers p of the form p=2^2+p1^2, where p1 is a prime. Find five such primes. (d) Every Fermat number Fn=2^2^n+1, where n ≥1, can be expressed as the sum of two squares. (e) Every odd perfect number (if one exists) is the sum o
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SOLVED:It has been conjectured that there are infinitely many primes of the form n^2-2 . Exhibit five such primes.
SOLVED:It has been conjectured that there are infinitely many primes of th…
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