Prove: in L number psiz 12, for every prime poiz, [p] = [1], [5) , [7) , or [11]

Q: 22] calculate the number of combination and permutation of, 5 distinct objects taken 2 at time?

A:

Q: Suppose that p, q are distinct prime numbers, prove that p9-1 + gp-1 = 1 mod pq

A: We use Fermat's Little Theorem, to prove our claim.

Q: b"=1 (mod n) is valid for which of the following pair (b,n) (9.7,1729) (97,1729) (-97,1729)…

A: Answer

Q: let x  be a fixed but arbitrary integer. Do there exist infinity many integer y such that,…

A: Let x = x0 be fixed given integer. Then,

Q: Let x be an integer. Prove that, if x mod 9 = 5, then 9|(x^2-2x+3)

A: Given: x mod 9=5 then, 9|x2-2x+3|

Q: Show that 2 is a primitive root modulo 3" for all n > 1.

A: To prove that 2 is a primitive root modulo 3n for all n≥1.

Q: I need help with this problem and an explanation for the solution described below (Discrete…

A: The objective of the question is to find the negation of the given statement. In logic, the negation…

Q: 2. What is the least residue of 610 C 512 10.4512 (mad 1112

A: Euler's theorem is used

Q: 5. Let a be a real number, c an integer, c > 0. Prove that

A:

Q: Find the least positive integer n that satisfies the congruence 7 ^128 congruent to n (mod13)

A: Given, 7128≡nmod 13 Find the value of n that satisfies the above congruence.

Q: п(п+1)(п+2) E}=1jG+ 1) = а. b. Prove that the sum of the first n Fibonacci numbers with odd indices…

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Q: 2. Encrypt the message STOP POLLUTION by translat- ing the letters into numbers, applying the given…

A: let's encrypt the message "STOP POLLUTION" using the given encryption functions one by one.For the…

Q: Prove that among 7 positive integers, there are always two integers such that either their sun or…

A:

Q: 7. Prove that every integer is congruent modulo 9 to a unique integer T such that -4≤r ≤ 4.

A:

Q: 122 is congruent to 5 modulo17 ?

A: To check whether -122 is congruent to 5 modulo 17 or not

Q: 5. Prove that every integer is congruent modulo 9 to one of the even integers 0, 2, 4, 6, ..., 16.

A: To prove that every integer is congruent modulo 9 to one of the even integers

Q: 17!=1(mod19). Select one: True False

A:

Q: . show that for every positive integer n, if n^2+2 is prime then n is a multuple of 3. Is the…

A:

Q: Show that y = x (mod p) leads to -y = -x (mod p).

A:

Q: Let {\mathcal S}S be the set of all (nonnegative) 4-digit integers. How many integers does {…

A: Here given S is set of all (nonnegative) 4-digit integers We have to calculate,  How many 4 digits…

Q: Suppose a, ne Z and 0 < a <n. Prove that n (2) = (^=¹1)+(21) a a-1 n- in two different ways: firstly…

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Q: Show that (-3) = 1 if q = ±1 mod 12 -1 if q = ±5 mod 12

A: