SOLUTION: determine whether it is possible for the sum of the squares of three consecutive numbers to ever be a square number
Algebra.Com
Question 430309: determine whether it is possible for the sum of the squares of three consecutive numbers to ever be a square number
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
If we let the integers be x, x+1, and x+2, then
. This number is congruent to 2 modulo 3, since is divisible by 3 and 5 is 2 modulo 3. Note that the perfect squares are either 0 or 1 modulo 3. This means that can never be equal to a perfect square.
RELATED QUESTIONS
The sum of the squares of two consecutive natural numbers is 85. Determine the... (answered by Gogonati)
Find three consecutive numbers, the sum of whose squares is 29 more than three times the... (answered by JulietG)
The sum of three consecutive EVEN number is 78.Determine the three... (answered by LauraGED,richwmiller)
The sum of squares of three consecutive odd numbers is 155. What are the... (answered by stanbon)
sum of the squares of three consecutive odd numbers is 2531.find the... (answered by Tatiana_Stebko)
The sum of the square of two consecutive natural numbers is 85. Determine the... (answered by richard1234)
(a) Find the smallest positive integer which can be written as the sum of
three, four,... (answered by math_helper,greenestamps)
A number n is 1 plus the sum of the squares of three consecutive odd integers. What is... (answered by jsmallt9)
A number n is 1 plus the sum of the squares of three consecutive odd integers. what is... (answered by vksarvepalli)