Number Theory – Page 6

abcd-is-a-four-digit-number-such-that-a-2-b-2-c-2-d-2-cd-and-cd-d-ab-Find-the-number-

Tinku Tara January 1, 2024 Number Theory 0 Comments

Question Number 202716 by Rasheed.Sindhi last updated on 01/Jan/24 $\overset{―}{a b c d} i s a f o u r d i g i t n u m b e r$ $s u c h t h a t a^{2} + b^{2} + c^{2} + d^{2} = \overset{―}{c d}$ $a n d \overset{―}{c d} - \overset{―}{d} = \overset{―}{a b} .$ $$\mathcal{F}{ind}\:{the}\:{number}.…

2025-2025-x-mod-17-

Tinku Tara December 6, 2023 Number Theory 0 Comments

Question Number 201418 by cortano12 last updated on 06/Dec/23 $2025^{2025} = x (\mod 17)$ Answered by mr W last updated on 06/Dec/23 $2025^{2025} (m o d 17)$ $$=\left(\mathrm{119}×\mathrm{17}+\mathrm{2}\right)^{\mathrm{2025}}…

2023-2023-mod-13-

Tinku Tara December 5, 2023 Number Theory 0 Comments

Question Number 201352 by cortano12 last updated on 05/Dec/23 $2023^{2023} = \dots (\mod 13)$ Answered by Rasheed.Sindhi last updated on 05/Dec/23 $2023^{2023} \equiv \dots (\mod 13)$ $$\mathrm{2023}^{\mathrm{2023}} \…

Let-abc-bca-cab-defg-where-a-b-g-are-decimal-digits-may-be-equal-to-0-Show-that-i-dg-a-b-c-ii-e-f-d-g-

Tinku Tara November 24, 2023 Number Theory 0 Comments

Question Number 200836 by Rasheed.Sindhi last updated on 24/Nov/23 $L e t \overset{―}{a b c} + \overset{―}{b c a} + \overset{―}{c a b} = \overset{―}{d e f g}$ $w h e r e a, b, \dots, g a r e d e c i m a l d i g i t s$ $(m a y b e e q u a l t o 0)$ $S h o w t h a t$ $$\left({i}\right)\overline {\:{dg}\:}={a}+{b}+{c}…

Show-that-abc-bca-cab-is-divisible-by-37-

Tinku Tara November 24, 2023 Number Theory 0 Comments

Question Number 200834 by Rasheed.Sindhi last updated on 24/Nov/23 $S h o w t h a t \overset{―}{a b c} + \overset{―}{b c a} + \overset{―}{c a b}$ $i s d i v i s i b l e b y 37$ Answered by AST last updated on 24/Nov/23 $$\mathrm{111}\left({a}+{b}+{c}\right)\:{is}\:{a}\:{multiple}\:{of}\:\mathrm{37}…

ab-b-ba-a-cde-ab-b-ba-a-f-a-b-c-d-e-f-are-all-different-and-in-some-order-consecutive-also-Determine-the-remain

Tinku Tara November 17, 2023 Number Theory 0 Comments

Question Number 200315 by Rasheed.Sindhi last updated on 17/Nov/23 ${\begin{cases} \overset{―}{a b} \cdot \overset{―}{b} + \overset{―}{b a} \cdot \overset{―}{a} = \overset{―}{c d e} \\ \overset{―}{a b} \cdot \overset{―}{b} - \overset{―}{b a} \cdot \overset{―}{a} = \overset{―}{f} \end{cases}$ $a, b, c, d, e, f a r e a l l d i f f e r e n t a n d i n$ $${some}\:{order}\:{consecutive}\:{also}. \…

Find-four-positive-integers-each-not-exceeding-70000-and-each-having-more-than-100-divisors-

Tinku Tara November 15, 2023 Number Theory 0 Comments

Question Number 200200 by Fridunatjan08 last updated on 16/Nov/23 $F i n d f o u r p o s i t i v e i n t e g e r s,$ $e a c h n o t e x c e e d i n g 70000 a n d$ $e a c h h a v i n g m o r e t h a n 100$ $d i v i s o r s .$ Answered by mr W last updated on…

By-strong-induction-prove-that-any-natural-number-equal-to-or-bigger-than-8-can-be-written-as-3a-5b-where-a-and-b-are-non-negative-integers-

Tinku Tara November 12, 2023 Number Theory 0 Comments

Question Number 200041 by depressiveshrek last updated on 12/Nov/23 $B y s t r o n g i n d u c t i o n p r o v e t h a t a n y$ $n a t u r a l n u m b e r e q u a l t o o r b i g g e r t h a n$ $8 c a n b e w r i t t e n a s 3 a + 5 b w h e r e a a n d b$ $a r e n o n - n e g a t i v e i n t e g e r s .$ Answered by des_ last updated on 12/Nov/23…

Find-the-remainder-n-1-2019-n-4-when-divide-by-53-

Tinku Tara November 10, 2023 Number Theory 0 Comments

Question Number 199864 by cortano12 last updated on 10/Nov/23 $Find the remainder \underset{n = 1}{\sum^{2019}} n^{4} when$ $divide by 53$ Answered by AST last updated on 10/Nov/23 $$\underset{{n}=\mathrm{1}}…

Find-the-number-of-positive-integers-that-are-factors-of-3-19-7-12-10-25-and-are-also-multiples-of-3-15-7-10-10-19-

Tinku Tara November 1, 2023 Number Theory 0 Comments

Question Number 199311 by necx122 last updated on 01/Nov/23 $F i n d t h e n u m b e r o f p o s i t i v e i n t e g e r s$ $t h a t a r e f a c t o r s o f 3^{19} . 7^{12} . 10^{25} a n d a r e$ $a l s o m u l t i p l e s o f 3^{15} . 7^{10} . 10^{19}$ Answered by AST last…

Category: Number Theory