Sum of squares (puzzle) — 2 comments

: Find 7 (not necessarily distinct) positive integers, at least one of which is greater than 1040, suc … more →

Tags: number puzzles

Sumbertime Views

: 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

: The sum of the squares of the first n natural numbers is:         … more →

Sums of squares using simple identities – (Part 2)

: 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

: 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 — 3 comments

: 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

: Goal:   To find   (a, b, c)   so that a   +   b   +   c   = … more →

Splitting the Sum of consecutive squares

: 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 — 1 comment

: 17   =   2^3   +   3^2   =   1^3   +   4^2 17   is the … more →

Palindromic Sums & Concatenation of Palindromes

: (1) As a sum of 2 squares: x   +   (x + 1)   =   2*x   +   1 x^2 … more →

Sums of squares using simple identities - (Part 1) — 2 comments

: 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 →

Tags: Math Beauty, Identities

Sum of squares of 4 consecutive integers

: 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

: (1)   Sum of squares of 2 consecutive integers expressed as the sum of 2 consecutive integers x^2 + … more →

Sum of even positive squares

:                  … more →

Concatenation : A || B = A^2 + B^2

: 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)

: 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

: 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

: 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 — 3 comments

: Sums of squares It’s a classical problem in number theory to ask which integers can be represe … more →

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