Num3er 75

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?

 
 
 

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About benvitalis

math grad - Interest: Number theory
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