I was struggling for ages on this question, and even after careful considering I cannot make sense of this with my knowledge of algebra or set theory.
How can I solve this?
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Have you tried to rewrite the equation in a factored form? – hardmath Mar 03 '21 at 17:48
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1This seems to me a number theory problem, not set theory. – lone student Mar 03 '21 at 17:49
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Where is this question from? – player3236 Mar 03 '21 at 18:16
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Complete the product, as in the linked dupe. – Bill Dubuque Mar 04 '21 at 00:03
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thanks for the advice @hardmath, I did spent hours rewrite the equation too. but I couldnt get nowhere. – Arale Mar 04 '21 at 10:10
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Thanks @line student, I corrected. – Arale Mar 04 '21 at 10:11
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hi @player3236., my teacher made this question. – Arale Mar 04 '21 at 10:12
1 Answers
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$$xy-2020x-2022y=1$$
$$(x-2022)(y-2020)=1+2020*2022$$
$$2020*2022+1=2021^2=(43*47)^2$$
$$x-2022=\pm(1,43,47,43^2,2021,47^2,2021^2)$$
Then you can just solve for x and y algebraically
mode_er
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1Also, every enumerated number can be $\pm$, e.g. $x - 2022 = -2021 = y - 2020$ gives a solution $(1, -1)$. – Dávid Laczkó Mar 03 '21 at 18:43
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