1979 AHSME Problems/Problem 22
Problem 22
Find the number of pairs of integers which satisfy the equation
.
Solution
Solution by e_power_pi_times_i
Notice that . Then
, and
. However,
will never be divisible by
, nor
, so there are
integer pairs of
.
Solution 2:
The equation is equivalent to . Taking mod 3, we get
or
which is a contradiction. Thus, the answer is
Solution by mickyboy789
See also
1979 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 21 |
Followed by Problem 23 | |
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