Suppose that a basket has n eggs in it. If the eggs aretaken from the basket...

 

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Suppose that a basket has n eggs in it. If the eggs aretaken from the basket 2,3,4,5, and 6 at a time, there remain1,2,3,4, and 5 eggs respectively. If the eggs are removed 7 at atime, then no eggs remain. What is the smallest value of nsuch that the above could occur? Assuming that a and b are integers not divisible by the prime pestablish the following: a. If aP=bP (mod p) then aEb(modp) b. If aP=bP (mod p) thenaP=bP (mod p2) Hint: By part a, a=b + pk for some k so thata?-bP = (b+bk) - bP;now show that p divides the latter expression. Suppose that a basket has n eggs in it. If the eggs aretaken from the basket 2,3,4,5, and 6 at a time, there remain1,2,3,4, and 5 eggs respectively. If the eggs are removed 7 at atime, then no eggs remain. What is the smallest value of nsuch that the above could occur? Assuming that a and b are integers not divisible by the prime pestablish the following: a. If aP=bP (mod p) then aEb(modp) b. If aP=bP (mod p) thenaP=bP (mod p2) Hint: By part a, a=b + pk for some k so thata?-bP = (b+bk) - bP;now show that p divides the latter expression.

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Assuming a and b are not divisable by p a if ab mod p then a b modp According to Fermats Theorem ... View the full answer