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Challenge You are given the numbers, 37 + n,
{37 + n.
natural numbers.
√n +144
Find the smallest value of n so that all of the numbers in the set are
The smallest value of n that makes all of the numbers in set natural numbers is

N Challenge You are given the numbers, 37 + n, {37 + n. natural numbers. √n +144 Find-example-1

1 Answer

6 votes

Answer: 25

Work Shown

12^2 = 144

13^2 = 169

169 - 144 = 25

If n = 25, then
√(n+144) = √(25+144) = √(169) = √(13^2) = 13 which is a natural number.

Also, if n = 25, then
(n)/(5) = (25)/(5) = 5 is also a natural number.

n = 25 is the smallest such number so that each expression results in a natural number. This is because 13^2 = 169 is the next largest perfect square compared to 12^2 = 144. Any other larger perfect squares will require larger values of n.

Other values of n that make each expression a natural number are:

n = 25, n = 145, n = 180, n = 340

There are likely infinitely many other such values of n.

User Opfau
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