Question Number 216995 by Rasheed.Sindhi last updated on 26/Feb/25 $$\mathrm{Find}\:\mathrm{all}\:\mathrm{prime}\:\mathrm{numbers}\:\:\mathrm{p}\:\mathrm{and}\:\mathrm{q}\: \\ $$$$\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{p}^{\mathrm{2}} −\:\:\mathrm{q}^{\mathrm{2}} =\:\:\mathrm{2024} \\ $$ Answered by Marzuk last updated on 26/Feb/25…
Question Number 216912 by ArshadS last updated on 26/Feb/25 $$\mathrm{Find}\:\mathrm{all}\:\mathrm{three}-\mathrm{digit}\:\mathrm{numbers}\:{n}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{1}.\:{n}\:\mathrm{is}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{the}\:\mathrm{sum}\:\:\mathrm{of}\:\:\mathrm{its}\:\:\mathrm{digits}. \\ $$$$\mathrm{2}.\:{n}\:\mathrm{is}\:\mathrm{a}\:\mathrm{perfect}\:\mathrm{square}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 216911 by ArshadS last updated on 24/Feb/25 $${Find}\:{all}\:{positive}\:{integer}\:\mathrm{x},\mathrm{y}\:{such}\:{that} \\ $$$$\mathrm{x}^{\mathrm{2}} +\:\mathrm{y}^{\mathrm{2}} +\:\mathrm{xy}\:=\:\mathrm{169} \\ $$ Answered by A5T last updated on 25/Feb/25 $$\mathrm{WLOG},\:\mathrm{let}\:\mathrm{x}\geqslant\mathrm{y} \\…
Question Number 216875 by ArshadS last updated on 23/Feb/25 $$\mathrm{Let}\:\:\mathrm{p}\:\:\mathrm{be}\:\mathrm{a}\:\mathrm{prime}\:\mathrm{number}\:\mathrm{greater}\:\mathrm{than}\:\mathrm{3}.\:\mathrm{Prove}\:\mathrm{that}\:\:\mathrm{p}^{\mathrm{2}} −\:\mathrm{1}\:\: \\ $$$$\mathrm{is}\:\:\mathrm{always}\:\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{24}. \\ $$ Answered by maths2 last updated on 23/Feb/25 $$\left({p}−\mathrm{1}\right)\left({p}+\mathrm{1}\right) \\ $$$$\mathrm{3}\mid\left({p}−\mathrm{1}\right)\left({p}+\mathrm{1}\right);{since}\:{p}\equiv\mathrm{1},\mathrm{2}\left[\mathrm{3}\right]…
Question Number 216783 by ArshadS last updated on 20/Feb/25 $${Find}\:{all}\:{positive}\:{integers}\:{n}\:{such}\:{that} \\ $$$${n}^{\mathrm{2}} +\mathrm{7}{n}+\mathrm{6}\:{is}\:{perfect}\:{square}. \\ $$ Answered by mehdee7396 last updated on 20/Feb/25 $${n}^{\mathrm{2}} +\mathrm{7}{n}+\mathrm{6}={k}^{\mathrm{2}} \\…
Question Number 216769 by ArshadS last updated on 19/Feb/25 $${Solve}\:{for}\:{integer}\:{k},{m}\:{and}\:{n}: \\ $$$${k}^{\mathrm{2}} {m}−{n}^{\mathrm{2}} =\mathrm{8} \\ $$ Answered by mehdee7396 last updated on 20/Feb/25 $$“\:{m}\:''\:{must}\:{be}\:\:{positive} \\…
Question Number 216664 by Rasheed.Sindhi last updated on 14/Feb/25 $$\mathrm{Solve}\:\mathrm{for}\:\mathrm{non}-\mathrm{negative}\:\mathrm{integers}: \\ $$$$\:\:\:\mathrm{n}^{\mathrm{3}} =\mathrm{3m}\left(\mathrm{m}+\mathrm{2n}+\mathrm{1}\right) \\ $$ Answered by AntonCWX last updated on 15/Feb/25 $${m}={n}=\mathrm{0} \\ $$…
Question Number 216538 by CrispyXYZ last updated on 10/Feb/25 $$\mathrm{Find}\:\mathrm{all}\:\mathrm{integer}\:\mathrm{solutions}\:\mathrm{of} \\ $$$$\mathrm{3}^{{m}} =\mathrm{2}{n}^{\mathrm{2}} +\mathrm{1}. \\ $$$$ \\ $$$${I}\:{only}\:{found}\:{m}=\mathrm{1},\:\mathrm{2},\:\mathrm{5}\:{by}\:{computer} \\ $$$${from}\:{m}=\mathrm{1}\:{to}\:{m}=\mathrm{30000}. \\ $$$${Is}\:{there}\:{any}\:{greater}\:{solutions}? \\ $$ Commented…
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Question Number 215272 by Rasheed.Sindhi last updated on 02/Jan/25 $$\begin{cases}{\overline {{abac}}=\left(\overline {{dc}}\right)^{\mathrm{2}} }\\{{d}=\frac{\overline {{ab}}}{{c}}}\\{{c}^{\mathrm{2}} =\overline {{ac}}}\end{cases} \\ $$$$\overline {{abac}}=? \\ $$ Answered by A5T last…