1023^x + x^1023 = 1024 .Find x.
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The difference is
(10^24 + x) - (10^23 - 7) which can also be written as:
(10^24 - 10^23) - (7 + x)
We know that , if both the terms are divisible by 3 then their difference is also divisible by 3 and also (10^x - 10^y) for x > y is always divisible by 3. Therefore, (7 + x) must be divisible by 3, the smallest value of x for which (7 + x) is divisible by 3 is x = 2.
Therefore, smallest value of x is 2.
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