Category: Number Theory

Question Number 196053 by mathlove last updated on 17/Aug/23 $$faindnterme$$$$4,-2,\frac{16}{9},-2,\dots \dots$$ Answered by Frix last updated on 17/Aug/23 $$\frac{16}{4},-2,\frac{16}{9},-2,\frac{16}{14},-2,\frac{16}{19},\dots$$$$\frac{\mathrm{16}}{\mathrm{4}},−\mathrm{2},\frac{\mathrm{16}}{\mathrm{9}},−\mathrm{2},\frac{\mathrm{16}}{\mathrm{16}},−\mathrm{2},\frac{\mathrm{16}}{\mathrm{25}},… \…

Question Number 194689 by cortano12 last updated on 13/Jul/23 Answered by MM42 last updated on 13/Jul/23 $$f_i:1,1,2,3,5,8,13,21,34,55,89,\dots$$$$\Rightarrow \mathrm{\forall }n=5k;5\mid f_n!!??$$$$\Rightarrow ifn<10000\to ans=4999✓$$$${if}\:\:{f}_{{n}}…

Question Number 193286 by BaliramKumar last updated on 09/Jun/23 $$\mathrm{Let}{}^{\prime }{\mathrm{P}}^{\prime }\mathrm{is}\mathrm{a}\mathrm{prime}\mathrm{number}(\mathrm{P}>1000).$$$$\mathrm{If}{}^{\prime }{\mathrm{P}}^{\prime }\mathrm{devided}\mathrm{by}1000,\mathrm{then}\mathrm{remainder}\mathrm{is}{}^{\prime }{\mathrm{r}}^{\prime }.$$$$\mathrm{How}\mathrm{many}\mathrm{value}\mathrm{of}{}^{\prime }{\mathrm{r}}^{\prime }?$$ Commented by Tinku Tara last updated on 09/Jun/23 $$\mathrm{All}\:\mathrm{number}\:\mathrm{other}\:\mathrm{than}\:\mathrm{multiple}…

Question Number 130109 by Adel last updated on 22/Jan/21 $$2+\frac{3}{2^3}+\frac{4}{3^3}+\frac{5}{4^3}+\frac{6}{5^3}+\cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot =?$$ Answered by Olaf last updated on 22/Jan/21 $$\mathrm{S}\:=\:\underset{{n}=\mathrm{1}} {\overset{\infty}…

Question Number 63674 by Tawa1 last updated on 07/Jul/19 $$\mathrm{Show}\mathrm{that}\mathrm{the}\mathrm{number}{122}^{\mathrm{n}}-{102}^{\mathrm{n}}-{21}^{\mathrm{n}}\mathrm{is}\mathrm{always}\mathrm{one}\mathrm{less}\mathrm{than}\mathrm{a}$$$$\mathrm{multiple}\mathrm{of}2020.\mathrm{For}\mathrm{every}\mathrm{positive}\mathrm{integer}\mathrm{n}.$$ Commented by Prithwish sen last updated on 07/Jul/19…