The factors of **75** are: 1 3 5 15 25 75

The prime factors are: 3 * 5 * 5

**75** is

1001011 in base 2

2210 in base 3

1023 in base 4 (the smallest pandigital number in base 4)

300 in base 5

203 in base 6

135 in base 7

113 in base 8

83 in base 9

69 in base 11

63 in base 12

5A in base 13

55 in base 14 (a repdigit number)

**75** is a deficient number

**75** is an evil number

**75** is a Lucky Number

**75** is a repfigit number or a Keith number

Fibonacci style sum: Digit sum

**75:**

**7** + **5** = 12

5 + 12 = 17

12 + 17 = 29

17 + 29 = 46

29 + 46 = **75**

**75^5 = 19^5 + 43^5 + 46^5 + 47^5 + 67^5**

**75** = 1^2 + 5^2 + 7^2

**75** = 5^2 + 5^2 + 5^2

**75** = 6^2 + 8^2 – 5^2

**75** = 10^2 – 5^2

**75** = 2^2 + 14^2 – 5^3

**75** = 10^2 + 10^2 – 5^3

**75** is the sum of consecutive positive integers in 5 ways:

**75** = 37 + 38

**75** = 24 + 25 + 26

**75** = 13 + 14 + 15 + 16 + 17

**75** = 10 + 11 + 12 + 13 + 14 + 15

**75** = 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12

Can you prove that there are infinitely many positive integers each of which is a sum of consecutive, positive integers in at least three ways?