A note on sums of five almost equal prime squares

Abstract.

Let N be any sufficiently large positive integer satisfying the congruence condition $N\equiv 5(\bmod \,24)$. It is shown that there exists a $\delta \ge 0$ such that N can be written as¶¶$\Biggl\{\matrix {N = p_1^2+ p_2^2+ p_3^2+ p_4^2+ p_5^2,\cr \Bigl|p_j-\sqrt {N\over 5}\Bigr|\leq U, j=1,2,3,4,5,\cr}$¶¶ where the p _i are prime numbers and U is chosen as $U = N^{{1 \over 2}-\delta }$.