3(22+1).(24+1).(28+1)......(232+1)+2
=(22-1)(22+1).(24+1).(28+1)......(232+1)+2
=(24-1).(24+1).(28+1)......(232+1)+2
=(28-1).(28+1)......(232+1)+2
=....
=(232-1)(232+1)+2
=264-1+2
=264+1
3 = 4 -1 = 22 -1 thay vào ta có :
\(\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)....\left(2^{32}+1\right)+2=\left(2^4-1\right)\left(2^4+1\right)...\left(2^{32}+1\right)+2\)
= \(=\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)+2=\left(2^{16}-1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)+2\)
\(=\left(2^{32}-1\right)\left(2^{32}+1\right)+2=2^{64}-1+2=2^{64}+1\)
3(22+1).(24+1).(28+1)......(232+1)+2
=(22-1)(22+1).(24+1).(28+1)......(232+1)+2
=(24-1).(24+1).(28+1)......(232+1)+2
=(28-1).(28+1)......(232+1)+2
=....
=(232-1)(232+1)+2
=264-1+2
=264+1
