
Steve S. answered 02/23/14
Tutor
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Tutoring in Precalculus, Trig, and Differential Calculus
a = 67, b = 30, and n = 7.
Verify and explain that (a - n) ≡ (mod b).
(67 - 7) ≡? (mod 30)
For this to be true, 67 - 7 must be an integer multiple of 30 (see Wolfram's ModularArithmetic or Wikipedia's Modular_arithmetic#Congruence_relation).
And it is: 67 - 7 = 60 = 2*30. Q.E.D.