Prove that if a + x ≡ a +y (mod n), then x ≡y (mod n)

Q: show that for all integers x and y (x-y)3=x3-y3(mod3)

A:

Q: Given 6x + 2 ≡ 101 (mod 7), find an integer z such that 2x ≡ z (mod 7)

A:

Q: if a equiv b (mod n) , then a⁴ equiv b⁴ (mod n) for any positive integer 4.

A:

Q: Find all Pnterers x such that 5x=12 (mat) LoxE 4 (mad) 7x=16 (modlo) and 1o00s x3000

A:

Q: True or False : a – c ≡ b – c (mod n) ⟺ a ≡ b (mod n)

A: We have to solve given problem:

Q: 3x = 1 (mod 6)

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

Q: (2x + 3 ) ≡ 8 mod 12

A: (2x + 3 ) ≡ 8 mod 12 x + 3 + 9 ≡ 8 +9 mod 12  2x + 12  ≡ 12 +5  mod 12

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

A:

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: x² + 4x = 10(mod11) (mod11) X=

A: Given that x2+4x≡10 (mod 11)x2+4x+4≡10+4 (mod 11)x2+4x+4≡14 (mod 11)x2+4x)(x+2)2≡14+11 (mod…

Q: True or False : 4x ≡ 12 (mod 10) ⟹ x ≡ 3 (mod 10)

A:

Q: x² + x = 13(mod17) X= * (mod17)

A:

Q: x² - 2x = 8(mod19) X= (mod19)

A:

Q: intervals on which f is concave up (down). Then

A: Given,            f(x)=5x-3x+6

Q: Find all integer values of x for which 3x = 4 (mod 8).

A: given congruence equation 3x≡4(mod 8)

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

A:

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

A:

Q: 5x² + 3x = 3(mod17) X = (mod17)

A: Given that 5x2+3x≡3 (mod 17)x(5x+3)≡3 (mod 17)x≡3 (mod 17)  or   (5x+3)≡3 (mod 17)x≡3 (mod 17)  or…

Q: If 3x = 6 mod 9, when -2 <x< 8. Then O x=(-1, 3, 5} x=(-1, 2, 5} O x=(-1, 2, 3} O x=(-1, 5, 6}

A:

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

A:

Q: Find all integers sx such that 2x = 5 (mod 7).

A:

Q: 2x² + 3x = 14(mod19) X = * (mod19)

A: Given,            2x2+3x≡14 (mod 19).

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

A:

Q: Show that if x mod 8 = 1, then (3x −5) mod 6 = 4.

A: Solution

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: true or false? explain this: 2 mod 5 ≡ 7 mod 5

A: a mod n  ≡ b mod n if n divides (a-b).

Q: Figure out how many solutions x² = x(mod n) has for n = 5,6,7 and then compute how many solutions…

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.