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\(If $a\equiv 16\pmod{37}$ and $b\equiv 21\pmod{37}$, then for what integer $n$ in the set $\{0,1,2,\ldots,35,36\}$ is it true that$$a-b\equiv n\pmod{37}~?$$ \)

 Nov 14, 2020
 #1
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n = 5.

 Nov 14, 2020
 #2
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a mod 37 = 16
b mod 37 = 21
(a - b) mod 37 = n, solve for n

 

a = 16  and  b = 21
(a - b) mod 37 = n


(16 - 21) mod 37 = - 5

n =37 + (-5) = 32

 Nov 14, 2020

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