253的16次方*187的19次方除以83的余数是多少?
问题描述：
253的16次方*187的19次方除以83的余数是多少?
答
253^15 * 187^19 (mod 83) = 4^15 * 21^19 (mod 83)
= 28^3 * 21 * 48^6 (mod 83)
=40*21*36^2 (mod 83)
= 10*51 (mod 83)
= 12 ( mod 83)
余数是12253^16* 187^19 (mod 83) = 4^16 * 21^19 (mod 83) = 7^4 * 21 * 48^6 (mod 83)=(-6)*21*36^2 (mod 83)= 40*51 (mod 83)= 48 ( mod 83) 余数是 48 4^16 (mod 83) = (4^4)^4 (mod 83) = (256 - 3*83)^4 (mod 83) = 7^4 (mod 83)