Quant Question Of The Day: 115
Integral Solutions
Find positive integral solutions for the equation: a! + b! + c! = 3d, where a ≤ b ≤ c.
See our previous ‘Questions of the Day’:
Quant Question Of The Day: 114
Quant Question Of The Day: 113
Find positive integral solutions for the equation: a! + b! + c! = 3d, where a ≤ b ≤ c.
For c > 5, c! is divisible by 9, say its 9k, then
3 + 9k = 3d
=> 3(3k + 1) = 3d
But 3d can never have any factor of form 3k + 1, so no solution for c> 5.
for c < 5 there are three solutions.
1!+2!+3!=3²
1!+2!+4!= 3³
1!+1!+1!= 3¹
Quant Question Of The Day: 114
Quant Question Of The Day: 113
a=b=c=d=1
only one solution