Problem
NT-B1-M11-P009 Impossible Remainder
#9
★★☆☆☆ Level 2 of 5
Prove that \(x^2+y^2=4z+3\) has no integer solutions.
Squares modulo \(4\) are only \(0\) and \(1\).
The left side modulo \(4\) can only be \(0,1,2\). The right side is \(3\pmod4\). Contradiction.
Basic impossibility by residues.