Blogs about: Sums Of Squares
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Every natural number which is a sum of rational squares is a sum of integer squares
Prove that every natural number which is a sum of rational squares is also a sum of integer squares. Let be a natural number and suppose . Then we have , so that is a sum of integer squares. Let be a… more →
Project Crazy Project
Sum of squares (puzzle)
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wrote 1 month ago: Find 7 (not necessarily distinct) positive integers, at least one of which is greater than 1040, suc … more →
Sumbertime Views
wrote 1 month ago: Like 666 (see Revelation 13:18), 153 (see John 21:11) appears in the Bible. And perhaps for the same … more →
Sum of the squares of the first n natural numbers
wrote 1 month ago: The sum of the squares of the first n natural numbers is: … more →
Sums of squares using simple identities – (Part 2)
wrote 1 month ago: Older post: Sums of squares using simple identities – (Part 1) #1 : 2(a^2 + b^2) = (b- … more →
Five consecutive integers whose sum is a perfect square
wrote 1 month ago: Five consecutive integers whose sum is N^2, a perfect square (N < 100) 3+4+5+6+7 = 25 … more →
Fibonacci numbers| a^2 + b^2 + c^2 + d^2 = e^2
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wrote 1 month ago: The Fibonacci Sequence is the series of numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, … more →
a^n + b^n + c^n, n=1,2,3
wrote 2 months ago: Goal: To find (a, b, c) so that a + b + c = … more →
Splitting the Sum of consecutive squares
wrote 2 months ago: older post: How to split the sum of consecutive integers into two equal sums The sum o … more →
Num3ers expressible as x^3 + y^2 in two distinct ways
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wrote 3 months ago: 17 = 2^3 + 3^2 = 1^3 + 4^2 17 is the … more →
Palindromic Sums & Concatenation of Palindromes
wrote 3 months ago: (1) As a sum of 2 squares: x + (x + 1) = 2*x + 1 x^2 … more →
Sums of squares using simple identities - (Part 1)
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wrote 3 months ago: The identities: #1 : 2(a^2 + b^2) = (b-a)^2 + (a+b)^2 #2 : 3(a^2 + b^2 + c^2) = (b-a)^ … more →
Sum of squares of 4 consecutive integers
wrote 4 months ago: Sum of squares of 4 consecutive integers expressed as the sum of 5 consecutive integers: (x – … more →
Sum of squares of consecutive integers expressed as the sum of 2 and 5 consecutive integers
wrote 4 months ago: (1) Sum of squares of 2 consecutive integers expressed as the sum of 2 consecutive integers x^2 + … more →
Sum of even positive squares
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Concatenation : A || B = A^2 + B^2
wrote 6 months ago: Concatenation is the joining of two numbers by their numerals. Concatenation of numbers A … more →
Set of Triples n, n+1,n+2; each is sum of two squares (including a puzzle)
wrote 6 months ago: For example, the triple of consecutive numbers (232, 233, 234) 232 = 6^2 + 14^2, 233 … more →
The circle method 2: Elementary estimates for the singular series for sums of 5 or more squares
wrote 1 year ago: This is the long-awaited second step in solving Waring’s problem continuing our study of the s … more →
The circle method 1: Sums of 5 or more squares
wrote 2 years ago: This is our first step in solving Waring’s problem. In particular, we’ll study the probl … more →
The circle method 0: Introducing Waring's problem
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wrote 2 years ago: Sums of squares It’s a classical problem in number theory to ask which integers can be represe … more →
