MathLabs

Problem 1

Find all integers a,b,c satisfying 1<a<b<c1<a<b<c such that (a−1)(b−1)(c−1)(a-1)(b-1)(c-1) is a divisor of abc−1abc-1.
Step 1 of 6: Introduce the positive quotient
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abc−1=q(a−1)(b−1)(c−1),q∈Z>0abc-1=q(a-1)(b-1)(c-1),\qquad q\in\mathbb Z_{>0}
Detailed analysis

The divisibility condition is equivalent to the displayed equation for a positive integer q.