Last digits
Number Theory
Level
3
Let C=(1976^1976-1974^1974)(1976^1975+1974^1973). A is equal to the sum of last 4 digits of C. Calculate A.
The answer is 0.
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any number ending with 6 raised to any number ends with 6;
any number ending with 4 raised to an even number ends with 6, and when raised to an odd number ends with 4.
C = (...6-...6)(...6+...6)
because the term in the first parenthesis is high, it will end in many zeros, that is (...0000)(.....12) ~ A = 0+0+0+0 = 0