Everything is not real

Number Theory Level 1

How many integer solution does the equation below has?

6 x + 51 y = 169 6x+51y=169


The answer is 0.

Fahim Muhtamim by Fahim Muhtamim , 17, Bangladesh

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3 solutions

Aruna Yumlembam
May 2, 2020

We observe that 51×4>169 this implies our y must be less than or equal to 3.We then do a trial as follows ,169-(51×3),169-(51×2),169-(51×1) and since non of the answers is divisible by 6,we conclude no answer.

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Daniele Prisco
Mar 19, 2020

gcd(6,51)=3, which doesn't divide 169, so there are no integer solutions to this equation.

1 Helpful 0 Interesting 1 Brilliant 0 Confused
Fahim Muhtamim
Oct 25, 2019

6 x + 51 y = 169 6x+51y=169 , therefore 2 x + 17 y = 169 3 2x+17y=\frac{169}{3} .

So all real solutions will not be integer.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

There is a typo on your RHS 169 3 \frac{169}{3}

Hana Wehbi - 1 year, 7 months ago

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