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13 November, 01:42

Prove that for all integers a and b, if a mod 7 = 5 and b mod 7 = 6 then ab mod 7 = 2.

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  1. 13 November, 04:29
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    Hello:

    if : a ≡ 5 (mod 7) ... (1)

    b ≡ 6 (mod 7) ... (2)

    (1) * (2) : ab ≡ 30 (mod 7)

    but : 30 = 7*4 + 2 ... so : 30 ≡ 2 (mod 7)

    then : ab ≡ 2 (mod 7)
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