# What is the smallest number that can be written as a sum of 2 squares in 3 ways?

Table of Contents

- 1 What is the smallest number that can be written as a sum of 2 squares in 3 ways?
- 2 What is the smallest positive integer that can be expressed as the sum of distinct integers?
- 3 What is the smallest number that can be expressed as the sum of two squares in two different ways?
- 4 Which is the smallest integer?
- 5 Which is the smallest square that can be expressed as the sum of two perfect squares?
- 6 How do you write a number as a sum of squares?

## What is the smallest number that can be written as a sum of 2 squares in 3 ways?

The following positive integers can be expressed as the sum of 2 square numbers in 3 distinct ways: 325,425,650,725,845,850,925,1025,1105,1250,…

## What is the smallest positive integer that can be expressed as the sum of distinct integers?

So, the smallest positive number that can be expressed as the sum of 2021 distinct integers is 1011.

**Which numbers can be written as the sum of two squares?**

All prime numbers which are sums of two squares, except 2, form this series: 5, 13, 17, 29, 37, 41, 53, 61, 73, 89, 97, 101, 109, 113, 137, 149, etc. Not only are these contained in the form 4n + 1, but also, however far the series is continued, we find that every prime number of the form 4n+1 occurs.

**What is the smallest number that can be expressed as the sum of two squares in two different ways you may use one square twice?**

The lowest integer that is the sum of two integer squares in two different ways is 50, but that case involves one repeat number 5^2 + 5^2 = 25 + 25 = 50 = 7^2 + 1.

### What is the smallest number that can be expressed as the sum of two squares in two different ways?

1729, the Hardy-Ramanujan Number, is the smallest number which can be expressed as the sum of two different cubes in two different ways. 1729 is the sum of the cubes of 10 and 9 – cube of 10 is 1000 and cube of 9 is 729; adding the two numbers results in 1729.

### Which is the smallest integer?

zero

The smallest integer is zero.

**What is the square of the smallest number that can be represented as a sum of two perfect squares and also two perfect cubes?**

1729

The same expression defines 1729 as the first in the sequence of “Fermat near misses” (sequence A050794 in the OEIS) defined, in reference to Fermat’s Last Theorem, as numbers of the form 1 + z3 which are also expressible as the sum of two other cubes.1729, the Hardy-Ramanujan Number, is the smallest number which can …

**What is the smallest number that can be expressed as the sum of two squares?**

Square Number

12 | 4 | 0, 1, 4, 9 |

13 | 7 | 0, 1, 3, 4, 9, 10, 12 |

14 | 8 | 0, 1, 2, 4, 7, 8, 9, 11 |

15 | 6 | 0, 1, 4, 6, 9, 10 |

16 | 4 | 0, 1, 4, 9 |

#### Which is the smallest square that can be expressed as the sum of two perfect squares?

Natural number which can be expressed as sum of two perfect squares in two different ways? Ramanujan’s number is 1729 which is the least natural number which can be expressed as the sum of two perfect cubes in two different ways.

#### How do you write a number as a sum of squares?

In number theory, the sum of two squares theorem relates the prime decomposition of any integer n > 1 to whether it can be written as a sum of two squares, such that n = a 2 + b 2 for some integers a, b. and k is odd.