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Divisibility Tests and Rules and Quotient Polynomials

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Let n be a positive integer

a) prove that n is divisible by 5 if and only if it ends with 0,5
b) prove than n is divisible by 11 if and only if the alternating sum of its digits is divisible by 11
c) find a similar criterion for divisibility by 7 and prove it .

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Divisibility Tests and Rules and Quotient Polynomials are investigated.

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