Number Theory – Page 56

find-all-possible-values-of-x-and-y-satisfying-1-2-3-x-y-2-

Tinku Tara June 3, 2023 Number Theory 0 Comments

Question Number 8302 by tawakalitu last updated on 07/Oct/16 $find all possible values of x and y satisfying$ $1! + 2! + 3! + \dots + x! = y^{2}$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Prove-that-there-are-infinite-prime-numbers-of-the-form-10-n-1-

Tinku Tara June 3, 2023 Number Theory 0 Comments

Question Number 8174 by prakash jain last updated on 02/Oct/16 $Prove that there are infinite prime$ $numbers of the form 10^{n} + 1$ Terms of Service Privacy Policy Contact: info@tinkutara.com

is-it-correct-when-S-n-1-2-1-3-1-4-1-5-1-n-2-3-2-4-2-5-2-n-3-4-3-5-3-n-4-5-4-n-

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Question Number 8139 by sou1618 last updated on 01/Oct/16 $i s i t c o r r e c t ?$ $w h e n$ $S_{n} = {$ $1 \times 2 + 1 \times 3 + 1 \times 4 + 1 \times 5 + \dots \dots . + 1 \times n$ $+ 2 \times 3 + 2 \times 4 + 2 \times 5 + \dots \dots . + 2 \times n$ $+ 3 \times 4 + 3 \times 5 + \dots \dots . + 3 \times n$ $+ 4 \times 5 + \dots \dots . + 4 \times n$ $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:….…

Find-the-remainder-if-49-1296-7-131-is-divided-by-13-

Tinku Tara June 3, 2023 Number Theory 0 Comments

Question Number 7859 by tawakalitu last updated on 21/Sep/16 $F i n d t h e r e m a i n d e r i f 49^{1296} \times 7^{131} i s d i v i d e d$ $b y 13$ Answered by sandy_suhendra last updated on 21/Sep/16 $$\mathrm{49}^{\mathrm{1296}} \:×\:\mathrm{7}^{\mathrm{131}}…

Given-that-Z-and-H-are-complex-number-obtain-the-real-and-imaginary-of-Z-H-

Tinku Tara June 3, 2023 Number Theory 0 Comments

Question Number 7748 by Tawakalitu. last updated on 13/Sep/16 $G i v e n t h a t Z a n d H a r e c o m p l e x n u m b e r .$ $o b t a i n t h e r e a l a n d i m a g i n a r y o f Z^{H}$ Answered by Yozzia last updated on 13/Sep/16 $L e t Z = {r e}^{i θ}, H = c + d i (r, θ, c, d \in R, r > 0, i = \sqrt{- 1}) .$ $${Z}^{{H}}…

w-x-y-z-are-digits-in-respective-base-system-and-a-b-are-bases-Find-out-an-example-examples-which-satisfy-the-following-wxyz-a-wxyz-b-wxyz-a-b-

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Question Number 7249 by Rasheed Soomro last updated on 19/Aug/16 $w, x, y, z a r e d i g i t s i n r e s p e c t i v e b a s e s y s t e m a n d$ $a, b a r e b a s e s .$ $F i n d o u t a n e x a m p l e / e x a m p l e s w h i c h s a t i s f y$ $t h e f o l l o w i n g$ ${w x y z}_{a} + {w x y z}_{b} = {w x y z}_{a + b}$ Commented…

An-Interesting-App-I-ve-recently-downloaded-the-app-called-Math-Tricks-from-the-Google-Play-Store-If-you-d-like-to-improve-your-speed-and-skill-in-the-mental-calculations-arena-I-think-this-app-s

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Question Number 7230 by Yozzia last updated on 17/Aug/16 $A n I n t e r e s t i n g A p p :$ $I^{'} v e r e c e n t l y d o w n l o a d e d t h e a p p c a l l e d$ $^{'} M a t h {T r i c k s}^{'} f r o m t h e G o o g l e P l a y S t o r e .$ $I f {y o u}^{'} d l i k e t o i m p r o v e y o u r s p e e d$ $a n d s k i l l i n t h e m e n t a l c a l c u l a t i o n s$ $a r e n a, I t h i n k t h i s a p p s h o u l d b e o f$ $i n t e r e s t t o y o u . T h e a p p c a n t h r o w y o u s i m p l e$ $${calculations}\:{that}\:{include}\:{the}\:{basic}\:{operations} \…

Let-a-and-b-be-positive-integers-such-that-ab-1-divides-a-2-b-2-Show-that-a-2-b-2-ab-1-is-the-square-of-an-integer-IMO-1988-Qu-6-

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Question Number 7213 by Yozzia last updated on 16/Aug/16 $L e t a a n d b b e p o s i t i v e i n t e g e r s s u c h$ $t h a t a b + 1 d i v i d e s a^{2} + b^{2} . S h o w t h a t$ $\frac{a^{2} + b^{2}}{a b + 1} i s t h e s q u a r e o f a n i n t e g e r .$ $(I M O 1988 Q u . 6)$ Terms of Service…

Evaluate-sin-3n-n-from-1-to-infinity-

Tinku Tara June 3, 2023 Number Theory 0 Comments

Question Number 7191 by Tawakalitu. last updated on 15/Aug/16 $E v a l u a t e Σ \frac{s i n (3 n)}{n} f r o m 1 t o i n f i n i t y$ Answered by Yozzia last updated on 15/Aug/16 $D e f i n e t h e f u n c t i o n$ $f (x) = x f o r 0 < x < 1, p e r i o d = 2 .$ $${For}\:{Fourier}\:{series}\:{of}\:{f}\:{having}\:{the}\:{form} \…

Evaluate-sin-n-n-From-1-to-infinity-

Tinku Tara June 3, 2023 Number Theory 0 Comments

Question Number 7189 by Tawakalitu. last updated on 15/Aug/16 $E v a l u a t e : Σ \frac{s i n (n)}{n}, F r o m 1 t o i n f i n i t y .$ Commented by Yozzia last updated on 15/Aug/16 $${f}\left({x}\right)=\frac{{a}_{\mathrm{0}} }{\mathrm{2}}+\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left\{{a}_{{n}} {cos}\frac{{n}\pi{x}}{{L}}+{b}_{{n}} {sin}\frac{{n}\pi{x}}{{L}}\right\}…

Category: Number Theory