Oblicz \(\displaystyle{ 3 ^{83}mod7}\).
Próbuję tak:
\(\displaystyle{ 3 ^{83}mod7=3 ^{80}*3 ^{3}mod7=27*3 ^{80}mod7=6*\left( 3 ^{2} \right) ^{40}mod7=}\)
\(\displaystyle{ =6*9 ^{40}mod7=6*2 ^{40}mod7=6*2*2 ^{39}mod7=12*\left( 2 ^{3} \right) ^{13}mod7=}\)
\(\displaystyle{ =5*8 ^{13}mod7=5*1 ^{13}mod7=5}\)
Zgadza się?
