Find two consecutive positive integers whose sum square is 365

x = 7 and x + 1 = 8 are the two consecutive numbers. The sum of the squares of two consecutive positive integers is equal to 145. Find the two numbers. Solution Two consecutive integers are of the form x and x + 1 The sum of their squares is equal to 145 x 2 + (x + 1) 2 = 145 Expand and group like terms in the above equation and write it in ...

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Five consecutive positive integers are added together. Find two positive numbers, x and y, whose sum is 64 and the sum of whose squares is a minimum.

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How many positive integers less than 60 have an even number of positive divisors? Guest Jun 30, 2019. If I remember correctly, ALL numbers between 2 and 59 have an EVEN numbers of positive divisors, EXCEPT the Perfect Squares, or 4, 9, 16, 25, 36 and 49, which have 3 divisors each.Determine all positive integers m for which there exists a positive integer 2 n such that ττ(n ) (n) = m. 49. (IMO ShortList 1999, Number Theory Problem 1) Find all the pairs of positive integers (x, p) such that p is a prime, x ≤ 2p and xp−1 is a divisor of (p − 1)x + 1. 50.


Jun 02, 2019 · The sum of the squares of the largest and smallest of three consecutive odd integers is 353 less than 3 times the square of the middle one. Find the integers. Math. 2. The sum of the reciprocals of two consecutive positive integers is 17/72. Write an equation that can be used to find the two integers. What are the integers? Consecutive odd integers are odd integers that follow each other in sequence. You may find it hard to believe, but just like even integers, a pair of any consecutive odd integers are also 2 units apart. Find two consecutive odd positive integers, sum of whose squares is 290.

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