Question

prove that in any primitive pythagorean triple (a,b,c), abc is a multiple of 30

Answer #1

Prove: If (a,b,c) is a primitive Pythagorean triple, then either
a or b is divisible by 3.

Prove: Let (a,b,c) be a primitive pythagorean triple. then we
have the following
1. gcd(c-b, c+b) =1
2. c-b and c+b are squares

The table of exercise 1 suggests that one of the numbers in any
primitive Pythagorean triple is divisible by 4, one is divisible by
3 and one is divisible by 5. Please Prove this

(a) Prove that if y = 4k for k ≥ 1, then there exists a
primitive Pythagorean triple (x, y, z) containing y.
(b) Prove that if x = 2k+1 is any odd positive integer greater
than 1, then there exists a primitive Pythagorean triple (x, y, z)
containing x.
(c) Find primitive Pythagorean triples (x, y, z) for each of z =
25, 65, 85. Then show that there is no primitive Pythagorean triple
(x, y, z) with z...

In class we proved that if (x, y, z) is a primitive Pythagorean
triple, then (switching x and y if necessary) it must be that (x,
y, z) = (m2 − n 2 , 2mn, m2 + n 2 ) for some positive integers m
and n satisfying m > n, gcd(m, n) = 1, and either m or n is
even. In this question you will prove that the converse is true: if
m and n are integers satisfying...

Prove: If (a, a+1, a+2) is a Pythagorean triple, then a= 3

Let a, b, c be natural numbers. We say that (a, b, c) is a
Pythagorean triple, if a2 + b2 = c2 . For example, (3, 4, 5) is a
Pythagorean triple. For the next exercises, assume that (a, b, c)
is a Pythagorean triple.
(c) Prove that 4|ab Hint: use the previous result, and a proof
by con- tradiction.
(d) Prove that 3|ab. Hint: use a proof by contradiction.
(e) Prove that 12 |ab. Hint : Use the...

Three positive integers (a, b, c) with a<b<c are called a
Pythagorean triple if the sum of the square of a and the square of
b is equal to the square of c. Write a program that prints all
Pythagorean triples (one in a line) with a, b, and c all smaller
than 1000, as well the total number of such triples in the end.
Arrays are not allowed to appear in your code. Hint: user nested
loops (Can you...

Three positive integers (a, b, c) with a<b<c are called a
Pythagorean triple if the sum of the square of a and the square of
b is equal to the square of c. Write a program that prints all
Pythagorean triples (one in a line) with a, b, and c all smaller
than 1000, as well the total number of such triples in the end.
Arrays are not allowed to appear in your code. Hint: user nested
loops (Can you...

Prove Pythagorean Theorem
a) Show at least 3 different proves if the Pythagorean
Theorem
b) Pythagorean triples with applications: indirect measurements
and mental math problems

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 41 minutes ago

asked 53 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 3 hours ago

asked 4 hours ago

asked 4 hours ago

asked 4 hours ago