Breaking Primes

Algebra Level 3

{ a b + c = 53 b c + a = 73 c a + b = 83 \begin{cases} ab + c = 53 \\ bc + a = 73 \\ ca + b = 83 \end{cases}

Let a , b a,b and c c be integers satisfying the system of equations above. What is the product a b c ? abc?


The answer is 462.

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Worranat Pakornrat by Worranat Pakornrat , 36, Thailand

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1 solution

a=7 b=6 c=11 Therefore abc=462

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