Determine the positive integer values of x less than 100 such that the last two digits of 2x equal x.
What positive integer values of y less than 100 are there such that the last two digits of 3y equal y?
Hi,
x would have to be a multiple of 4, and 2^4n always ends in 6, so the only possibilities are 16, 36, 56, 76 and 96. Since the last 2 digits of powers repeat at intervals of 20, it just remains to check the last 2 digits of 2^16, which are 36.
Hence, the only possible value for x is 36.
y would have to be odd, and this would mean y ends in 3 or 7. Again inspecting the first 20 powers of 3, we find that the only possible solution for y is 87.
|
|
Posted by nirmal
on 2006-08-08 17:17:01 |
Solution for both x and y
