ruthiealvarez6320 ruthiealvarez6320
  • 18-09-2017
  • Mathematics
contestada

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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ghanami
ghanami ghanami
  • 18-09-2017
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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