Equation with factorial: x^2 + y^2 + z^2 + t^2 = 2018!

[Gosia]

Prove, that if positive integers x, y, z, t satisfy the equation:

x^2 + y^2 + z^2 + t^2 = 2018!

, each of the numbers x, y, z, t are greater than 10^250.

2018! is the factorial of 2018
2018!=1*2*3*4*...*2017*2018

Does anyone have any idea?

 

[mmm4444bot]

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We're interested to know whether you have any ideas. Have you tried or thought about anything specific? Maybe consider a simpler version, first. :cool: