2s and 5s together make fun
Number Theory
Level
2
(2222^5555) + (5555^2222) is divisible by two of the given numbers.Enter the bigger number as your answer.
9
7
2
5
3
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1 solution
2222^{5555}+4^{5555}+5555^{2222}-4^{2222}-4^{5555}+4^{2222}
(2222^{5555} +4^{5555} is divisible by 2226 and so by 7) (5555^{2222} -4^{2222} is divisible by 5551 and so by 7) = -4^{2222}(4^{3333}-1) =4^{2222}(64^{1111}-1^{1111})
(64^{1111}-1 is divisible by 63 therefore by7) [SO THE WHOLE NUMBER IS DIVISIBLE BY 7]