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Number Theory Level 3

The number of positive integral solutions of x 4 − y 4 = 3789108 x^{4}-y^{4}=3789108 is

1 2 Infinitely many 0

Rishabh Tripathi by Rishabh Tripathi , 22, India

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3 solutions

Adhiraj Dutta
Apr 7, 2020

good 'ol graph good 'ol graph

1 Helpful 1 Interesting 1 Brilliant 0 Confused
Prakhar Uniyal
Jan 17, 2018

If both the variables are Odd(/Even) the expression x^{4}-y^{4} will be a multiple of 8.

If only one of them was odd then the expression would be equal to an odd term.

As the given number is neither an odd one nor a multiple of 8, there can be no solutions.

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Mr Yovan
Mar 11, 2016

All natural numbers ^4 are either 6,1 or 5 mod 10 The result is 8 mod 10 It is impossible to get 8 mod 10 using only either 6,1 or 5 mod 10

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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