Question Number 217066 by ArshadS last updated on 28/Feb/25 $${Find}\:{all}\:{integer}\:{x},{y}\:{such}\:{that} \\ $$$${x}^{\mathrm{2}} −{y}^{\mathrm{2}} =\mathrm{100} \\ $$ Answered by mehdee7396 last updated on 28/Feb/25 $$\left({x}−{y}\right)\left({x}+{y}\right)=\mathrm{2}×\mathrm{50}=\mathrm{10}×\mathrm{10} \\…
Question Number 217030 by ArshadS last updated on 27/Feb/25 $$\mathrm{Find}\:\mathrm{all}\:\mathrm{positive}\:\mathrm{integers}\:\:\mathrm{n}\:\:\mathrm{such}\:\mathrm{that}\:\: \\ $$$$\:\mathrm{n}\:+\:\mathrm{1}\:\:\mathrm{divides}\:\:\mathrm{n}^{\mathrm{2}} \:+\:\mathrm{1} \\ $$ Answered by issac last updated on 27/Feb/25 $$\frac{{n}+\mathrm{1}}{{n}^{\mathrm{2}} +\mathrm{1}}=\frac{{n}+\mathrm{1}}{\left(\mathrm{1}+{n}\boldsymbol{{i}}\right)\left(\mathrm{1}−{n}\boldsymbol{{i}}\right)} \\…
Question Number 217040 by ArshadS last updated on 27/Feb/25 $$\mathrm{Find}\:\mathrm{all}\:\mathrm{positive}\:\mathrm{integers}\:\:\mathrm{n}\:\:\mathrm{such}\:\mathrm{that} \\ $$$$\:\:\mathrm{n}\:\:\mathrm{divides}\:\:\mathrm{2}^{{n}} \:+\:\mathrm{1}.\:\: \\ $$ Answered by Ghisom last updated on 27/Feb/25 $$\mathrm{one}\:\mathrm{group}\:\mathrm{of}\:\mathrm{solutions}\:\mathrm{is}\:{n}=\mathrm{3}^{{k}} \wedge{k}\in\mathbb{N} \\…
Question Number 216995 by Rasheed.Sindhi last updated on 26/Feb/25 $$\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 $${m}={n}=\mathrm{0} \\ $$…