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Category: Number Theory

Let-n-j-q-Z-1-Are-there-triples-n-j-q-such-that-the-following-conditions-are-satisfied-altogether-i-n-j-q-ii-n-2-j-2-q-2-Suppose-then-that-condition-ii-

Question Number 5144 by Yozzii last updated on 19/Apr/16 $${Let}\:{n},{j},{q}\in\left(\mathbb{Z}^{+} −\left\{\mathrm{1}\right\}\right).\:{Are}\:{there}\: \\ $$$${triples}\:\left({n},{j},{q}\right)\:{such}\:{that}\:{the}\:{following} \\ $$$${conditions}\:{are}\:{satisfied}\:{altogether}? \\ $$$$\left({i}\right)\:{n}={j}^{{q}} \:\:\:\: \\ $$$$\left({ii}\right){n}^{\mathrm{2}} ={j}^{\mathrm{2}} +{q}^{\mathrm{2}} \\ $$$$−−−−−−−−−−−−−−−−−−−−−− \\…

Question-5125

Question Number 5125 by Rojaye Shegz last updated on 16/Apr/16 Commented by Rojaye Shegz last updated on 16/Apr/16 $$\mathrm{Sorry},\:\mathrm{that}\:\mathrm{was}\:\mathrm{an}\:\mathrm{error}. \\ $$$$\frac{\mathrm{p}}{\mathrm{q}}\:\mathrm{is}\:\mathrm{the}\:\left\{\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{p}+\mathrm{q}−\mathrm{1}\right)\left(\mathrm{p}+\mathrm{q}−\mathrm{2}\right)+\mathrm{p}\right\}\mathrm{th}\:\mathrm{term} \\ $$ Commented by…

If-x-y-z-is-a-primitive-Pythagorean-triple-prove-that-x-y-and-x-y-are-congruent-modulo-8-to-either-1-or-7-

Question Number 70525 by Rasheed.Sindhi last updated on 05/Oct/19 $${If}\:{x},{y},{z}\:{is}\:{a}\:{primitive}\:{Pythagorean} \\ $$$${triple},{prove}\:{that}\:{x}+{y}\:{and}\:{x}−{y}\:{are} \\ $$$${congruent}\:{modulo}\:\mathrm{8}\:{to}\:{either}\:\mathrm{1}\:{or}\:\mathrm{7}. \\ $$ Answered by mind is power last updated on 07/Oct/19…

If-gcd-p-q-1-prove-that-gcd-p-p-q-q-p-q-pq-1-Related-to-Q-69939-

Question Number 70370 by Rasheed.Sindhi last updated on 04/Oct/19 $${If}\:\:{gcd}\left({p}\:,\:{q}\right)=\mathrm{1},{prove}\:{that} \\ $$$$\:\:\:\:\:{gcd}\left({p}\left({p}+{q}\right)\:,\:{q}\left({p}+{q}\right)\:,\:{pq}\right)=\mathrm{1} \\ $$$$\mathrm{R}\boldsymbol{\mathrm{elated}}\:\boldsymbol{\mathrm{to}}\:\boldsymbol{\mathrm{Q}}#\mathrm{69939} \\ $$ Commented by mind is power last updated on 03/Oct/19…