Show that: if a = b(mod n) and C = d\modn), then a +c =b+d\mod n)!

Q: If a = b (mod m) and a = b (mod n) then a = b (mod mn)

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Q: If cy (mod n) andc>0 then a) x= y (mod cn) b) x y (mod n) ) xy d) (mod") None of these

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Q: If a cy (mod n) and c> 0 then a) x y (mod en) b) x y (mod n) ) x=y (mod) d) None of these :Select…

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Q: 3x = 1 (mod 6)

A: 3x≡1 (mod 6) ⇒ 3x-1≡0 (mod 6)This means 3x-1 is divisible by 6.

Q: 1. Find all x, y, and z such that a) x = 3 (mod 4) x = 5 (mod 21) x = 7 (mod 25) b) 3y = 9 (mod 12)…

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Q: If x = 2 (mod 5) and y = 4 (mod 5) then 2x – 3y =? (mod 5)

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Q: Suppose that a and b are integers. a ≡ 7 (mod 13) and b ≡ 9 (mod 13). Find the integer c such that 0…

A: The given problem is to find the modular values of c for the given conditions with given integers a…

Q: Show that if a ≡ b (mod m) and c ≡ d (mod m), then a + c ≡ b + d (mod m).

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Q: The system 2x + 3y = 4 (mod 4) 3x + 4y = 5 (mod 4) has no solution modulo 4. Select one: True False

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Q: 4 If a = b (mod n), then a" = b™ (mod n) for every positive integer m.

A: It is given that  a≡b (mod n), then am≡bm (mod n) for every positive integer m. It will prove by…

Q: Find  mod (40, 7) and div (40, 7).   mod(40, 7)=? div(40, 7)=?

A: 1) mod(40,7)  is the remainder when 40 is divided by 7we know that 7×5 =35  and 7×6=42as 7×6=42 is…

Q: If a≡3 (mod 11) and b≡9 (mod 11): (a) Compute a+b(mod 11) (b) Compute a^3(mod 11)

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Q: IfOcy (mod n) and e> 0 then a) *= y (mod cn) b) x= y (mod n) ) x=y (mod) d) None of these :Select…

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Q: Show that 18! ≡ -1 (mod 437).

A: We have to show that: 18!≡-1mod437

Q: Find  mod (59, 10) and div (59, 10).

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

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Q: 53!=r(mod61)

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

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Q: If a = b (mod n) and b = c (mod n) then which of the following is false. a =c (mod n) a = c (mod n)…

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Q: If a+c=b+c (mod m) then a =b (mod m) Select one: True False

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Q: Let a,b,and c be natural numbers and n be a natural number > 0. Prove that if a = b mod n, then a^c…

A: Use mathematical induction to prove the given statement.

Q: Find the nonnegative integer a less than 28 represented by each of these pairs, where each pair…

A: According to the given information, it is required to find the non-negative integer a less than 28…

Q: If nez then I89?bmodm a=+b moad m

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Q: (f) If a = b (mod n), then a* bk (mod n) for any positive integer k.

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Q: Let x, y ∈Z. Prove that if x≡1(mod 5) and y ≡2(mod5 ), then x^2-y^2≡0(mod 5).  Give 2 examples to…

A: Given, x,y∈ℤ and x≡1mod 5, y≡2mod 5

Q: Prove that (50!)2 mod 101 = -1 mod 101.

A: We have to prove that 50!2mod101=-1 mod101.

Q: Q2/let n be a fixed positive integer and a,b be arbitrary integers. Then a = b (modn) iffa and b…

A: We have to prove that Given statement

Q: For n=195, by Fermat's theorem a-2 a) a' (modn) b) 1(modn) c) 0(modn) d) a(mod n)

A: Fermat's theorem

Q: Fand all Pntegers x such that Sx=!2 (mod チ) LOXEA (modst) 子« =16 (modlo)

A: We have to find all integers such that  5x≡12mod 7         . . . (1) 10x≡4mod 11         . . . (2)…