Question and Answers Forum

Number TheoryQuestion and Answers: Page 16

Question Number 70525 Answers: 1 Comments: 0

If x,y,z is a primitive Pythagorean triple,prove that x+y and x−y are congruent modulo 8 to either 1 or 7.

$I f x, y, z i s a p r i m i t i v e P y t h a g o r e a n$ $t r i p l e, p r o v e t h a t x + y a n d x - y a r e$ $c o n g r u e n t m o d u l o 8 t o e i t h e r 1 o r 7 .$

Question Number 70370 Answers: 1 Comments: 4

If gcd(p , q)=1,prove that gcd(p(p+q) , q(p+q) , pq)=1 Related to Q#69939

$I f g c d (p, q) = 1, p r o v e t h a t$ $g c d (p (p + q), q (p + q), p q) = 1$ $You can't use 'macro parameter character #' in math mode$

Question Number 70145 Answers: 1 Comments: 0

prove that ; arg(z1z2)=arg(z1)+arg(z2). arg(z1/z2)=arg(z1)−arg(z2).

$p r o v e t h a t; a r g (z 1 z 2) = a r g (z 1) + a r g (z 2) .$ $a r g (z 1 / z 2) = a r g (z 1) - a r g (z 2) .$

Question Number 70138 Answers: 1 Comments: 0

prove that e^(iθ) =e^(i(θ+2kΠ)) given that k=0,±1,±2...

$p r o v e t h a t e^{i θ} = e^{i (θ + 2 k Π)} g i v e n t h a t k = 0, \pm 1, \pm 2 . . .$

Question Number 69574 Answers: 1 Comments: 0

Question Number 69571 Answers: 1 Comments: 0

Question Number 69569 Answers: 2 Comments: 0

Question Number 69567 Answers: 0 Comments: 2

Question Number 67193 Answers: 0 Comments: 7

Question Number 66275 Answers: 0 Comments: 2

Prove that for p,q,r∈N ((lcm(p,q,r))/(gcd(p,q,r)))=((p×q×r)/(gcd(p,q)×gcd(q,r)×gcd(r,p)))

$P r o v e t h a t f o r p, q, r \in N$ $\frac{lcm (p, q, r)}{\gcd (p, q, r)} = \frac{p \times q \times r}{\gcd (p, q) \times \gcd (q, r) \times \gcd (r, p)}$

Question Number 63917 Answers: 0 Comments: 2

lim_(x→∞) ((√(x+(√(x+(√x)))))−(√x))

$\lim_{x \to \infty} (\sqrt{x + \sqrt{x + \sqrt{x}}} - \sqrt{x})$

Question Number 63674 Answers: 0 Comments: 2

Show that the number 122^n − 102^n − 21^n is always one less than a multiple of 2020. For every positive integer n.

$Show that the number 122^{n} - 102^{n} - 21^{n} is always one less than a$ $multiple of 2020 . For every positive integer n .$

Question Number 62554 Answers: 0 Comments: 0

If a & b are two natural numbers then the following relation holds always. a×b=gcd(a,b)×lcm(a,b) ^• If a,b & c are three natural numbers what relation(anologous to the above) holds between numbers and their gcd & lcm?

$I f a & b a r e t w o n a t u r a l n u m b e r s$ $t h e n t h e f o l l o w i n g r e l a t i o n h o l d s$ $a l w a y s .$ $a \times b = \gcd (a, b) \times lcm (a, b)$ $^{∙} I f a, b & c a r e t h r e e n a t u r a l n u m b e r s$ $w h a t r e l a t i o n (a n o l o g o u s t o t h e a b o v e)$ $h o l d s b e t w e e n n u m b e r s a n d t h e i r$ $\gcd & lcm ?$

Question Number 62244 Answers: 1 Comments: 3

Find out x,y, such that gcd(x^3 ,y^2 )=gcd(x^2 ,y^3 )

$Find out x, y, such that$ $\gcd (x^{3}, y^{2}) = \gcd (x^{2}, y^{3})$

Question Number 62242 Answers: 2 Comments: 1

Find out x,y such that lcm(x,y)=180 ∧ gcd(x,y)=45

$Find out x, y such that$ $lcm (x, y) = 180 \land \gcd (x, y) = 45$

Question Number 62214 Answers: 1 Comments: 0

Find out x,y such that ((lcm(x,y))/(gcd(x,y)))=lcm(x,y)−gcd(x,y)

$Find out x, y such that$ $\frac{lcm (x, y)}{\gcd (x, y)} = lcm (x, y) - \gcd (x, y)$

Question Number 57933 Answers: 0 Comments: 0

Question Number 55701 Answers: 1 Comments: 1

Is true or not that 4181 is the only one Fibonacci′s number with no prime factor which is also a Fibonacci′s number?

$I s t r u e o r n o t t h a t 4181 i s t h e o n l y o n e$ ${F i b o n a c c i}^{'} s n u m b e r w i t h n o p r i m e f a c t o r$ $w h i c h i s a l s o a {F i b o n a c c i}^{'} s n u m b e r ?$

Question Number 55631 Answers: 1 Comments: 0

Question Number 55476 Answers: 1 Comments: 0

4 metal rods of length 78 cm,104 cm,117cm, a.nd 169 cm are to be cut into parts of equal length Each length must be as long as possible What is the maximum number of pieces that can be cut?

$4 m e t a l r o d s o f l e n g t h 78 c m, 104 c m, 117 c m,$ $a . n d 169 c m a r e t o b e c u t i n t o p a r t s o f e q u a l l e n g t h$ $E a c h l e n g t h m u s t b e a s l o n g a s p o s s i b l e$ $W h a t i s t h e m a x i m u m n u m b e r o f p i e c e s$ $t h a t c a n b e c u t ?$

Question Number 54897 Answers: 2 Comments: 1

Find value of n so 120 ∣ 5n(n^2 −1)

$Find value of n so 120 ∣ 5 n (n^{2} - 1)$

Question Number 53620 Answers: 1 Comments: 4

Σ_(n=0) ^∞ (((−1)^n )/(2n+1)) =? 1. (π/4) 2. (π^2 /(12)) 3. (π/8) 4. (π^2 /6)

$\underset{n = 0}{\sum^{\infty}} \frac{{(- 1)}^{n}}{2 n + 1} = ?$ $1 . \frac{π}{4} 2 . \frac{π^{2}}{12} 3 . \frac{π}{8} 4 . \frac{π^{2}}{6}$

Question Number 53618 Answers: 1 Comments: 3

Let x,y∈Z if x^2 +y^2 divide xy+1 then prove ((x^2 +y^2 )/(xy+1)) is square of integer number

$Let x, y \in Z$ $if x^{2} + y^{2} divide xy + 1 then prove$ $\frac{x^{2} + y^{2}}{xy + 1} is square of integer number$

Question Number 53048 Answers: 0 Comments: 1

Question Number 51507 Answers: 0 Comments: 0

^• 739 is a prime number and its reversed number 937 is also prime. Determine 4-digit prime numbers whose reversed be also prime. ^• If number of such primes is a function of number of digits, determine that the function is increasing or not.

$^{∙} 739 i s a p r i m e n u m b e r a n d$ $i t s r e v e r s e d n u m b e r 937 i s a l s o$ $p r i m e .$ $D e t e r m i n e 4 - d i g i t p r i m e n u m b e r s$ $w h o s e r e v e r s e d b e a l s o p r i m e .$ $^{∙} I f n u m b e r o f s u c h p r i m e s i s a$ $f u n c t i o n o f n u m b e r o f d i g i t s,$ $d e t e r m i n e t h a t t h e f u n c t i o n i s$ $i n c r e a s i n g o r n o t .$

Question Number 50960 Answers: 0 Comments: 0

4 (3) 2 5 3 (?) 1 1 6 1 2 (8) ? ? 1 find numbers of each ?

$4 (3) 2$ $5 3 (?) 1 1$ $6 1 2 (8) ? ? 1$ $find numbers of each ?$

Pg 11 Pg 12 Pg 13 Pg 14 Pg 15 Pg 16 Pg 17 Pg 18 Pg 19 Pg 20

Contact: info@tinkutara.com