Question 1197923
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<pre>

It is easy to check directly that  567288133  gives the remainder  5  when divided by  8.

By the way, for it, only three last digits of a number are important.


    We write  567288133 == 5 mod 8.


It means that {{{567288133^6}}}  gives the remainder  {{{5^6}}} when divided by 8.


    Next,  {{{5^6}}} = 15625.


It is also easy to check directly that the remainder  {15625 mod 8}  is the same as  {1 mod 8}.

    (and again, for it, only three last digits of the number 15625 do matter).


<U>ANSWER</U>.  When the number {{{(567288133)^6}}} is divided by 8, the remainder is 1.
</pre>

Solved.



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May the god save you from solving this problem in the way as @MathLover1 does it . . .