Question

7.1 A common factor of (527^379 + 473^379) and (527^166 - 473^166) is:​

Answer 1

Answer:

527 as it is in the both.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

Step-by-step explanation:

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.(X^n - Y^n) is divisible by both ( x+a)& ( x - a ) if n is even,

Please be clear.