Difference between revisions of "Talk:1988 IMO Problems/Problem 6"
(Possible approach with Chinese Remainder Theorem?) |
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In case of <math>GCD(a,b) = d>1</math> we can transform quotient to <math>d^2((a_1)^2 + (b_1)^2)/(d^2a_1b_1 + 1)</math> where <math>a_1 = a/d</math> and <math>b_1 = b/d</math> and follow the same reasoning as above. | In case of <math>GCD(a,b) = d>1</math> we can transform quotient to <math>d^2((a_1)^2 + (b_1)^2)/(d^2a_1b_1 + 1)</math> where <math>a_1 = a/d</math> and <math>b_1 = b/d</math> and follow the same reasoning as above. | ||
| − | It's just an idea without final and rigorous proof yet. | + | It's just an idea without final and rigorous proof yet and it may contain counterexample gaps. |
Am I mistaken? | Am I mistaken? | ||
Help :) | Help :) | ||
Revision as of 07:55, 2 July 2024
I just wonder if it's possible to solve this problem with Chinese Remainder Theorem
First: assuming that 
.
Then quotient is always square 
and 
and is less or equal than 
and is not divisible by neither 
nor 
which implies it's square of integer.
In case of 
we can transform quotient to 
where 
and 
and follow the same reasoning as above.
It's just an idea without final and rigorous proof yet and it may contain counterexample gaps.
Am I mistaken?
Help :)
