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The product of the last two digits of (1919)1919 is
63
The last two digits are the remainder on division by 100.
(1919)1919 = (1920 - 1)1919
= -1 + 1919C1(1920) - 1919C2(1920)2 +
Every term from (1920)2 onwards is divisible by 19202, hence by 100.
(1919)1919 1919 1920 - 1 100
1919 1920 = 3684480 80 100
(1919)1919 80 - 1 = 79 100
Last two digits are 7 and 9; product = 7 9 = 63
Answer: 63
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