281487861809153 ≡ 281 x 1000^4 + 487 x 1000^3 + 861 x 1000^2 + 809 x 1000^1 + 153 x 1000^0 (mod 999)

∵ X^n ≡ 1 (mod X-1) , Piggy's(GATI) little theorem

281487861809153 ≡ 281 x 1 + 487 x 1 + 861 x 1 + 809 x 1 + 153 x 1 (mod 999)

281487861809153 ≡ 281 + 487 + 861 + 809 + 153 ≡ 593 (mod 999)

65537^2 = 4295098369

42+95+09+83+69 = 199 -> 100 -> 1

4295098369 ÷ 99 = 43384832.010101...

4+295+098+369 = 766

4295098369 ÷ 999 = 4299397.766766...

42+9509+8369 = 17920 -> 7921

4295098369 ÷ 9999 = 429552.79217921...

65537^(65537+1) = Z -> -> 最後的數是...1 (!)

65537^65537 = Z -> -> 最後的數是...1 (!)

*66+1=67
67^1 =67
67^2 = 4489 -> 34
67^3 = 300763 -> 100 ->1
67^4 = 20151121 -> 67(!)
67^5 = 1350125107 -> 133 -> 34
67^6 = 90458382169 -> 199 -> 100 -> 1
67^7 = 6060711605323 -> 6+06+07+11+60+53+23 = 166 -> 67(!)
*33+1 = 34
34^1 = 34
34^2 = 1156 -> 67
34^3 = 39304 -> 100 -> 1
34^4 = 1336336 -> 1+33+63+36 = 133 -> 34 (!)
34^5 = 45435424 -> 45+43+54 +24 = 166 -> 67
34^6 = 1544804416 -> 15+44+80+44+16 = 199 ->100 ->1
34^7 = 52523350144 -> 5+25+23+35+01+44 = 133 -> 34(!)
*667^1 = 667
667^2 = 444889 -> 1333 -> 334
667^3 = 296740963 -> 1999 -> 1000 -> 1
667^4 = 197926222321 -> 1666 -> 667 (!)
667^5 = 132016790288107 -> 1333 -> 334
*334^1 = 334
334^2 = 111556 -> 667
334^3 = 37259704 -> 1000 -> 1
334^4 = 12444741136 -> 1333 -> 334 (!)
334^5 = 4156543539424 -> 1666 -> 667