Competition problem — Number theory

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Number theory Difficulty 5.9 AIME, harder Prove it

28. Show that the product of two integers of the form $4 k+1$ is again of this form, while the product of two integers of the form $4 k+3$ is of the form $4 k+1$ .

Solution

None

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.