Posted by **rakesh** on Saturday, December 13, 2008 at 5:42am.

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 -
**Reiny**, Saturday, December 13, 2008 at 8:17am
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

527^{379} + 473^{379}

= (527+473)(some big number)

= 1000(some big number)

527^{166} - 473^{166}

= (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

## Answer This Question

## Related Questions

- math - find the greatest common factor and simplify your answer. 4v to the 7th ...
- algebra2 plzz help - how do you solve these problems (5x)to the power of a+4(5x)...
- mathematics - [{(3 to power 5by2*5 to power 3by4)/2to power -5by4}/{16/5 to ...
- college - let i = the square root of -1 with i to the 1st power =i, i to the 2nd...
- physics - The disk shaped head of a pin is 1.0 mm in diameter. Which of the ...
- math - simplify, 4v to the 7th power y to the 9th power and 16v to the 6th power...
- Algebra - Factor each of following expressions x (4th power) - x (3rd power) - ...
- math - 4v to the 7th power y to the 9th power and 16v to the 6th power x to the ...
- government - what is the ordinance power of the president a. the power to send u...
- government - the power that allows congress to take private property for such ...

More Related Questions