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Number TheoryQuestion and Answers: Page 11

Question Number 115742 Answers: 1 Comments: 0

what the cooefficient of x^(10) from (1+x)×(1+2x^2 )×(1+3x^3 )×...×(1+2020x^(2020) )

$w h a t t h e c o o e f f i c i e n t o f x^{10} f r o m$ $(1 + x) \times (1 + 2 x^{2}) \times (1 + 3 x^{3}) \times . . . \times (1 + 2020 x^{2020})$

Question Number 115033 Answers: 2 Comments: 0

If a and b positive real number where a^(505) + b^(505) = 1, then minimum value a^(2020) + b^(2020) is __

$I f a a n d b p o s i t i v e r e a l n u m b e r w h e r e$ $a^{505} + b^{505} = 1, t h e n m i n i m u m v a l u e$ $a^{2020} + b^{2020} i s__$

Question Number 114401 Answers: 1 Comments: 0

What is reminder when 4^(29) divided by 17

$W h a t i s r e m i n d e r w h e n 4^{29}$ $d i v i d e d b y 17$

Question Number 114130 Answers: 1 Comments: 5

Question Number 113221 Answers: 0 Comments: 3

Does anyone know a good website for nested radicals? ((7((20))^(1/3) −19))^(1/6) =((5/3))^(1/3) −((2/3))^(1/3)

$D o e s a n y o n e k n o w a g o o d$ $w e b s i t e f o r n e s t e d r a d i c a l s ?$ $\sqrt[6]{7 \sqrt[3]{20} - 19} = \sqrt[3]{5 / 3} - \sqrt[3]{2 / 3}$

Question Number 113199 Answers: 1 Comments: 8

Change the following decimal number into binary number: 73.108

$C h a n g e t h e f o l l o w i n g d e c i m a l$ $n u m b e r i n t o b i n a r y n u m b e r :$ $73.108$

Question Number 113187 Answers: 1 Comments: 0

a,b,c ∈N such that ((a(√3) +b)/(b(√3)+c)) ∈ Q, show that ((a^2 +b^2 +c^2 )/(a+b+c)) ∈ Z

$a, b, c \in N such that \frac{a \sqrt{3} + b}{b \sqrt{3} + c} \in Q, show$ $that \frac{a^{2} + b^{2} + c^{2}}{a + b + c} \in Z$

Question Number 113134 Answers: 3 Comments: 2

any one can explain me how to change decimal number to biner number. i′m forgot. example (315)_(10) = (...)_2 thank you

$any one can explain me how to$ $change decimal number to$ $biner number . i^{'} m forgot .$ $example {(315)}_{10} = {(. . .)}_{2}$ $thank you$

Question Number 113101 Answers: 0 Comments: 2

Prove that GCD ((a,b),b)=(a,b)

$P r o v e t h a t G C D ((a, b), b) = (a, b)$

Question Number 113091 Answers: 1 Comments: 0

What is the area bounded by the curves arg(z) = (π/3) ; arg(z)= ((2π)/3) and arg(z−2−2i(√3))=π on the complex plane?

$What is the area bounded by the curves$ $\arg (z) = \frac{π}{3}; \arg (z) = \frac{2 π}{3} and \arg (z - 2 - 2 i \sqrt{3}) = π$ $on the complex plane ?$

Question Number 113073 Answers: 1 Comments: 0

Find all positive integers n for which 5^n +1 is divisible by 7

$Find all positive integers n for$ $which 5^{n} + 1 is divisible by 7$

Question Number 113006 Answers: 1 Comments: 0

a+(1/(b+(1/(c+(1/(d+...))))))=(2)^(1/3) If a,b,c,d,... are positive integers, then what is the value of ′b′?

$a + \frac{1}{b + \frac{1}{c + \frac{1}{d + . . .}}} = \sqrt[3]{2}$ $If a, b, c, d, . . . are positive integers, then$ $what is the value of^{'} b^{'} ?$

Question Number 113005 Answers: 1 Comments: 0

Two different two−digit natural numbers are written beside each other such that the larger number is written on the left. When the absolute difference of the two numbers is subtracted from the four−digit number so formed, the number obtained is 5481. What is the sum of the two−digit numbers?

$Two different two - digit natural$ $numbers are written beside each$ $other such that the larger number$ $is written on the left . When the$ $absolute difference of the two$ $numbers is subtracted from the$ $four - digit number so formed, the$ $number obtained is 5481 . What is the$ $sum of the two - digit numbers ?$

Question Number 113003 Answers: 1 Comments: 2

The digits of a three−digit number A are written in the reverse order to form another three−digit number B. If B>A and B−A is perfectly divisible by 7. Find the range of values of A.

$The digits of a three - digit number A$ $are written in the reverse order to$ $form another three - digit number B .$ $If B > A and B - A is perfectly$ $divisible by 7 . Find the range of$ $values of A .$

Question Number 113002 Answers: 1 Comments: 0

After distributing sweets equally among 25 children, 8 sweets remained. Had the number of children been 28, 22 sweets would have been left after equally distributing. What was the total number of sweets?

$After distributing sweets equally$ $among 25 children, 8 sweets$ $remained . Had the number of children$ $been 28, 22 sweets would have been$ $left after equally distributing . What$ $was the total number of sweets ?$

Question Number 113001 Answers: 0 Comments: 1

N! is completely divisible by 13^(52) . What is the sum of the digits of the smallest such number N?

$N! is completely divisible by 13^{52} .$ $What is the sum of the digits of the$ $smallest such number N ?$

Question Number 113000 Answers: 1 Comments: 0

The first 23 natural numbers are written in an increasing order beside each other to form a single number. What is the remainder when this number is divided by 18?

$The first 23 natural numbers$ $are written in an increasing order$ $beside each other to form a single$ $number . What is the remainder when$ $this number is divided by 18 ?$