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Find a common factor of (527 to the power 379 + 473 to the power 379) and (527 to the power 166 - 473 to the power 166)

  • indices -

    did you know that for

    x^n + y^n, x + y is a factor if n is odd and for
    x^n - y^n, x-y is a factor in n is even

    e.g. try some small numbers that fit into your calculator for testing

    5^7 + 11^7 = 19565296 and
    19565296 divides by 16 evenly 1222831 times

    13^6 - 5^6 = 4811184 and
    4811184 divides by 8 evenly 601398 times

    I will use this property

    527379 + 473379
    = (527+473)(some big number)
    = 1000(some big number)

    527166 - 473166
    = (527-473)(some other big number)
    = 54(some other big number)

    so the first one divides by 1000, the other by 54,

    so a common factor is 2

    note it said to find "a common" factor, not the highest common factor.
    There may be others

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