Question

Show that there are infinitely many pairs integers a and b with gcd(a, b) = 5...

Show that there are infinitely many pairs integers a and b with gcd(a, b) = 5 and a + b = 65

Homework Answers

Answer #1

Here I'm using gcd(a,b)=5 definition gives 5|a and 5|b.and using divides defination a=5k1 and b=5k2 for k1 ,k2 be integers.answer is below thank you.

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
(a) If a and b are positive integers, then show that gcd(a, b) ≤ a and...
(a) If a and b are positive integers, then show that gcd(a, b) ≤ a and gcd(a, b) ≤ b. (b) If a and b are positive integers, then show that a and b are multiples of gcd(a, b).
Calculate the gcd of 11639881 and 243 and express it in the form gcd(11639881, 243)= 11639881x...
Calculate the gcd of 11639881 and 243 and express it in the form gcd(11639881, 243)= 11639881x + 243y. Can you find another pair of integers s and t distinct from x and y s.t. gcd=11639881s + 243t? Can you find infinitely many such distinct pairs? I'm struggling to answer the second part of the question. The answer I got for the first pair is x= -98 and y=4694273 (gcd=1).
Calculate the gcd of 11639881 and 243 and express it in the form gcd(11639881, 243)= 11639881x...
Calculate the gcd of 11639881 and 243 and express it in the form gcd(11639881, 243)= 11639881x + 243y. Can you find another pair of integers s and t distinct from x and y s.t. gcd=11639881s + 243t? Can you find infinitely many such distinct pairs? I'm struggling to answer the second part of the question. The answer I got for the first pair is x= -98 and y=4694273 (gcd=1).
Prove there are infinitely many negative integers.
Prove there are infinitely many negative integers.
Show that if a and b are positive integers where a is even and b is...
Show that if a and b are positive integers where a is even and b is odd, then gcd(a, b) = gcd(a/2, b).
Show that there are infinitely many primes of the form 6n + 5.
Show that there are infinitely many primes of the form 6n + 5.
Show that there are infinitely many primes of the form 6n+5
Show that there are infinitely many primes of the form 6n+5
(a) If a and b are positive integers, then show that lcm(a, b) ≤ ab. (b)...
(a) If a and b are positive integers, then show that lcm(a, b) ≤ ab. (b) If a and b are positive integers, then show that lcm(a, b) is a multiple of gcd(a, b).
Prove that for all non-zero integers a and b, gcd(a, b) = 1 if and only...
Prove that for all non-zero integers a and b, gcd(a, b) = 1 if and only if gcd(a, b^2 ) = 1
4. Let a, b, c be integers. (a) Prove if gcd(ab, c) = 1, then gcd(a,...
4. Let a, b, c be integers. (a) Prove if gcd(ab, c) = 1, then gcd(a, c) = 1 and gcd(b, c) = 1. (Hint: use the GCD characterization theorem.) (b) Prove if gcd(a, c) = 1 and gcd(b, c) = 1, then gcd(ab, c) = 1. (Hint: you can use the GCD characterization theorem again but you may need to multiply equations.) (c) You have now proved that “gcd(a, c) = 1 and gcd(b, c) = 1 if and...