Product = Sum

Algebra Level 3

How many unordered non-zero integer solutions are there to the following equation?

a b c = a + b + c abc=a+b+c

An infinite number of solutions No solutions 2 solutions A finite number of solutions greater than two 1 solutions

Mikaeel Shah by Mikaeel Shah , 15, United Kingdom

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1 solution

Roberto Gomide
Jul 24, 2018

1+2+3=(1) (2) (3)

-1-2-3=(-1) (-2) (-3)

I found these examples,but I don't really have a rigorous proof.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

a=1, b=2, c=3

a=-1, b=-2, c=-3

but a,b,c are exchangeable, so total solution should be 3!*3!=12

Jian Hau Chooi - 2 years, 10 months ago

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You're right

Roberto Gomide - 2 years, 10 months ago

please report this question

Jian Hau Chooi - 2 years, 10 months ago

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