Can you find a number that is both a multiple of 2, but not a multiple of 4 and which happens to be a perfect square?
Answer: No. using modular arithmetic.
We have the equation from the data given which is:
4n + 2 = x²: where n and x are real numbers.
Taking the mod from both sides we obtain:\
4n+2(mod 4) = x²(mod 4)
0 +2 = x²(mod 4)
2 = x²(mod 4)
computing x from 0-3, we obtain:
x = 0: x² = 0
x=1: x² =1
x=2:x² = 4
x =3: x²=9
we see that x² does not equal 4 and since we are using modular arithmetic of 4, this means that the results of x² are periodic over intervals of 4, thus we cannot find a solution to the equation.
numberdot 