Category: Number Theory

Question Number 14614 by RasheedSoomro last updated on 03/Jun/17 $$\mathrm{If}5{\mathrm{doesn}}^{\prime }\mathrm{t}\mathrm{divide}\mathrm{any}\mathrm{of}\mathrm{n},\mathrm{n}+1,$$$$\mathrm{n}+2,\mathrm{n}+3\mathrm{then}\mathrm{prove}\mathrm{that}$$$$\mathrm{n}(\mathrm{n}+1)(\mathrm{n}+2)(\mathrm{n}+3)\equiv 24\left(\mathrm{mod}100\right)$$ Commented by mrW1 last updated on 03/Jun/17 $$\mathrm{n}\:\mathrm{doesn}'\mathrm{t}\:\mathrm{divide}\:\mathrm{n}? \…

Question Number 145408 by Dwaipayan Shikari last updated on 04/Jul/21 $${\int }_0^x\lfloor u\rfloor (\lfloor u\rfloor +1)f\left(u\right)du=\underset{n=1}{\sum ^{\lfloor x\rfloor }}n{\int }_n^{x}f\left(u\right)du$$$$Provethat$$ Terms of Service Privacy…

Question Number 13744 by AH Soomro last updated on 23/May/17 $$Solvethefollowing$$$$7^x\equiv 13\left(mod18\right)$$$$Plgivecompleteprocess.$$ Commented by prakash jain last updated on…

Question Number 13728 by prakash jain last updated on 22/May/17 $$\mathrm{Prove}\mathrm{that}$$$$\mathrm{n}!>{\left(\frac{n}{3}\right)}^n$$ Answered by mrW1 last updated on 23/May/17 $$Usingmathematicalinduction:$$$${for}\:{n}=\mathrm{1}\:{we}\:{have}…

Question Number 13724 by prakash jain last updated on 22/May/17 $$\mathrm{Expansion}\mathrm{of}1000!\mathrm{has}249,0^{\prime }s\mathrm{at}\mathrm{the}\mathrm{end}$$$$\mathrm{Find}\mathrm{the}\mathrm{first}\mathrm{non}-\mathrm{zero}\mathrm{digit}\mathrm{from}$$$$\mathrm{right}.$$$$1000!=\dots \dots d000\dots 00$$$$\mathrm{What}\mathrm{is}\mathrm{the}\mathrm{value}\mathrm{of}d?$$ Commented by prakash jain…