Remainder

2¹ ≡ 2 (mod 100)

2² ≡ 4 (mod 100)
2³ ≡ 8 (mod 100)
2⁴≡ 16 (mod 100)
2⁵ ≡ 32 (mod 100)
2⁶ ≡ 64 (mod 100)
2⁷ ≡ 28 (mod 100)
2⁸ ≡ 56 (mod 100)
2⁹ ≡ 12 (mod 100)
2¹º ≡ 24 (mod 100)
2¹¹ ≡ 48 (mod 100)
2¹² ≡ 96 (mod 100)
2¹³ ≡ 92 (mod 100)
2¹⁴≡ 84 (mod 100)
2¹⁵ ≡ 68 (mod 100)
2¹⁶ ≡ 36 (mod 100)
2¹⁷ ≡ 72 (mod 100)
2¹⁸ ≡ 44 (mod 100)
2¹⁹ ≡ 88 (mod 100)
2²º ≡ 76 (mod 100)
2²¹≡ 52 (mod 100)

2²² ≡ 4 (mod 100)
...........

∴ 98^123456 (mod 100)
≡ 2^123456 (mod 100)
≡ 2^(1 + 123440 + 16) (mod 100)
≡ 2^16 (mod 100)
≡ 36


2012-05-30 00:51:46 補充：
Corr:

≡ 2^(1 + 123440 + 16) (mod 100)
should be :


≡ 2^(1 + 123440 + 15) (mod 100)
≡ 2^16 (mod 100)
≡ 36