Question

Heya

# Pikaachu was out of town -_-

# Maths Aryabhattas 0_0 Solving my previous questions ? Here you go with more :p

Find all integer solutions to the Diophantine Equation :

${n}^{2} - n + 2nk - 3k + {k}^{2} = 40190$

Good luck

Answer 1

This is Diophantine equation, so all unknowns will take integer values.

We got :
$k = \frac{ {m}^{2} }{2} - \frac{m}{2} - 20095$
where m ,n, k are integer.
Either
$n = - \frac{ { m}^{2} }{2} - \frac{m}{2} + 20096$
or


$n = - \frac{ { m}^{2} }{2} + \frac{3m}{2} + 20095$

For example, take m= 1
k= -20095
n= 20095. or 20096

For More explanation see pic.