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Number TheoryQuestion and Answers: Page 21

Question Number 15835 Answers: 0 Comments: 1

Number of decimal digits in 50! is

$Number of$ $decimal digits$ $in 50! is$

Question Number 15789 Answers: 0 Comments: 0

Prove that: 2^(2^(2n + 1) ) + 2^2^(2n) + 1 , is never a prime for any positive n.

$Prove that : 2^{2^{2 n + 1}} + 2^{2^{2 n}} + 1, is never a prime for any positive n .$

Question Number 15788 Answers: 0 Comments: 2

Find all rational solution of the equation a + b = ab

$Find all rational solution of the equation a + b = ab$

Question Number 15787 Answers: 0 Comments: 2

Find the four digits number such that 4 ∙ abcd = dcba

$Find the four digits number such that 4 \cdot abcd = dcba$

Question Number 15742 Answers: 1 Comments: 1

This question is posted on the request of mrW1 (See comments of my answer to Q#15543). Find the last last non-zero digit of the expansion of 2000!

$This question is posted on the request of mrW 1$ $You can't use 'macro parameter character #' in math mode$ $Find the last last non - zero digit of the expansion$ $of 2000!$

Question Number 15543 Answers: 2 Comments: 0

Q#13724 Reposted. E_ ^ xpansion of 1000! has 24 0′s at the end. Find the first non- zero digit from right. 1000!=....d0000...0 What is the the value of d?

$You can't use 'macro parameter character #' in math mode$ $E_{}^{} xpansion of 1000!$ $has 24 0^{'} s at the end . Find$ $the first non - zero digit$ $from right .$ $1000! = . . . . d 0000 . . . 0$ $What is the the value of d ?$

Question Number 15377 Answers: 1 Comments: 0

−39 mod 4 = ?

$- 39 \mod 4 = ?$

Question Number 15322 Answers: 0 Comments: 6

Question Number 15292 Answers: 3 Comments: 0

Light version of Q#13724 Expansion of 100! has 24, 0′s at the end. Find the first non-zero digit from right. 100!=.....d000...00 What is the value of d?

$You can't use 'macro parameter character #' in math mode$ $E xpansion of 100! has 24, 0^{'} s at the end .$ $Find the first non - zero digit from right .$ $100! = . . . . . d 000 . . . 00$ $What is the value of d ?$

Question Number 14949 Answers: 0 Comments: 2

Find the largest prime factor of 203203. Anyone please suggest the method without calculators or log tables.

$Find the largest prime factor of 203203 .$ $Anyone please suggest the method$ $without calculators or \log tables .$

Question Number 14715 Answers: 2 Comments: 2

Find the remainder when 55^(99) is divided by 14

$Find the remainder when 55^{99} is divided by 14$

Question Number 14614 Answers: 1 Comments: 2

If 5 doesn′t divide any of n,n+1, n+2,n+3 then prove that n(n+1)(n+2)(n+3)≡24(mod100)

$If 5 {doesn}^{'} t divide any of n, n + 1,$ $n + 2, n + 3 then prove that$ $n (n + 1) (n + 2) (n + 3) \equiv 24 (\mod 100)$

Question Number 14757 Answers: 1 Comments: 0

Solve: ((1000!)/(5×10×15×...1000))≡x(mod 10)

$Solve :$ $\frac{1000!}{5 \times 10 \times 15 \times . . . 1000} \equiv x (\mod 10)$

Question Number 14419 Answers: 0 Comments: 0

Question Number 13744 Answers: 1 Comments: 4

Solve the following 7^x ≡13(mod 18) Pl give complete process.

$S o l v e t h e f o l l o w i n g$ $7^{x} \equiv 13 (m o d 18)$ $P l g i v e c o m p l e t e p r o c e s s .$

Question Number 13733 Answers: 0 Comments: 4

Question continuing from mrW1 post on p^2 mod n≡1. Find a number n such that for all m<n such that HCF(m,n)=1 m^2 mod n =1 e.g. for 12 possible value of m are 1,5,7,11.

$Question continuing from$ $mrW 1 post on p^{2} \mod n \equiv 1 .$ $Find a number n such that$ $for all m < n such that HCF (m, n) = 1$ $m^{2} \mod n = 1$ $e . g . for 12 possible value of m$ $are 1, 5, 7, 11 .$

Question Number 13728 Answers: 1 Comments: 0

Prove that n!>((n/3))^n

$Prove that$ $n! > {(\frac{n}{3})}^{n}$

Question Number 13725 Answers: 0 Comments: 2

(1/7)=.142857^(−) (1/7) is a recurring decimal of period 6. What will be the period of (1/7^(20) )?

$\frac{1}{7} = . \overset{―}{142857}$ $\frac{1}{7} is a recurring decimal of period 6 .$ $What will be the period of \frac{1}{7^{20}} ?$

Question Number 13724 Answers: 2 Comments: 3

Expansion of 1000! has 249, 0′s at the end Find the first non−zero digit from right. 1000!=......d000...00 What is the value of d?

$Expansion of 1000! has 249, 0^{'} s at the end$ $Find the first non - zero digit from$ $right .$ $1000! = . . . . . . d 000 . . . 00$ $What is the value of d ?$

Question Number 13606 Answers: 1 Comments: 0

Show that 19^(93) − 13^(99) is a positive integer divisible by 162.

$Show that 19^{93} - 13^{99} is a positive$ $integer divisible by 162 .$

Question Number 13584 Answers: 2 Comments: 10

Calculate 19^(93) (mod 81).

$Calculate 19^{93} (\mod 81) .$

Question Number 13529 Answers: 0 Comments: 7

Let p be a prime number > 3. What is the remainder when p^2 is divided by 12?

$Let p be a prime number > 3 . What$ $is the remainder when p^{2} is divided by$ $12 ?$

Question Number 13141 Answers: 1 Comments: 3

Question Number 13121 Answers: 1 Comments: 0

Find the value of : (2/(15)) + (2/(35)) + (2/(63)) + (2/(99)) + ... + (2/(9999))

$Find the value of : \frac{2}{15} + \frac{2}{35} + \frac{2}{63} + \frac{2}{99} + . . . + \frac{2}{9999}$

Question Number 13102 Answers: 0 Comments: 4

Find the sum of the nth term : 1^6 + 2^6 + 3^6 + 4^6 + ... + n^6

$Find the sum of the nth term : 1^{6} + 2^{6} + 3^{6} + 4^{6} + . . . + n^{6}$

Question Number 12861 Answers: 2 Comments: 0

change0.356^− into p/q form

$c h a n g e 0.35 \bar{6} i n t o p / q f o r m$

Pg 16 Pg 17 Pg 18 Pg 19 Pg 20 Pg 21 Pg 22 Pg 23 Pg 24 Pg 25

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