I recently took a test for a math competition for fun and I wasn't quite sure how to solve this problem.
The test is long over but I still remember the question which is as follows:
If X^2 + Y^2 + Z^7 = 2017 and X, Y, AND X, Y, and Z are positive integers, THEN
What is the sum of the values of X, Y, and Z?
It was a multiple choice question and the answers were 59 - 63 I believe
a) 59 b) 60 c) 61 d) 62 e) 63
First I tested what possible values for Z could exist.
**I tried Z = 1 which is 1^7 = 1
**I tried Z = 2 which is 2^7 = 128
**I tried Z = 3 which is 3^7 = 2187
This means the value of Z is 1 or 2. Z can not be zero because zero is neither positive nor negative (I assume?)
I then tested the upper bound for an integer that could exist that would be less than 2017
I came up with:
**44^2 = 1936
**45^2 = 2025
So a maximum integer value of 44 is possible for X or Y and a Maximum value of 2 is possible for Z.
I'm not really sure where to go from here though.. I tried plugging in Z = 2 and Z = 1 into the equation then solving for Y. The zero for the equation doesn't graph out to an integer.
Ie y = sqrt(2016 - X^2) for Z = 1 or y = sqrt(1889 - X^2) for Z = 2.
Any suggestions or pointers would be appreciated. I'm interested in this problem just out of curiosity.
The test is long over but I still remember the question which is as follows:
If X^2 + Y^2 + Z^7 = 2017 and X, Y, AND X, Y, and Z are positive integers, THEN
What is the sum of the values of X, Y, and Z?
It was a multiple choice question and the answers were 59 - 63 I believe
a) 59 b) 60 c) 61 d) 62 e) 63
First I tested what possible values for Z could exist.
**I tried Z = 1 which is 1^7 = 1
**I tried Z = 2 which is 2^7 = 128
**I tried Z = 3 which is 3^7 = 2187
This means the value of Z is 1 or 2. Z can not be zero because zero is neither positive nor negative (I assume?)
I then tested the upper bound for an integer that could exist that would be less than 2017
I came up with:
**44^2 = 1936
**45^2 = 2025
So a maximum integer value of 44 is possible for X or Y and a Maximum value of 2 is possible for Z.
I'm not really sure where to go from here though.. I tried plugging in Z = 2 and Z = 1 into the equation then solving for Y. The zero for the equation doesn't graph out to an integer.
Ie y = sqrt(2016 - X^2) for Z = 1 or y = sqrt(1889 - X^2) for Z = 2.
Any suggestions or pointers would be appreciated. I'm interested in this problem just out of curiosity.