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K divided by 21 divided by N is equivalent to divided by?

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โˆ™ 2009-01-20 23:51:35
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Q: K divided by 21 divided by N is equivalent to divided by?
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23. If the remainder when a number n is divided by m is r, then it is written as n ≡ r MOD m (read as "n is equivalent to r modulo m") and n = mk + r for some integer k. if n ≡ 643 MOD 837, then n = 837k + 643 (for some k) When n is divided by 31: n ÷ 31 = (837k + 643) ÷ 31 = 837k ÷ 31 + 643 ÷ 31 = 27k + 20 + 23/31 Multiplying both sides by 31: → n = 31 x (27k + 20) + 31 x 23/31 = 31m + 23 (where m = 27k + 20) → n ≡ 23 MOD 31 Thus the remainder when the same number is divided by 31 is 23.


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