154=44+64+84+94+144
15 = 4 × 4 − 4 ÷ 4 = 44 ÷ 4 + 4
15 = 123 − 45 + 6 − 78 + 9
15 = 98 − 76 − 5 − 4 + 3 − 2 + 1
15 = 0^2 + 1^8 + 2^7 − 3^9 + 4^5 + 5^6 + 6^1 + 7^4 + 8^3 + 9^0
a(n) = 3*n*(n + 3)/2. (n = 2)
4 9 2
3 5 7
8 1 6
3rd Order LoShu Magic Square with Sum 15. The Antipodal pairs sum to 10, (4 + 6, 2 + 8, 9 + 1, 3 + 7)
Problem : Order 15 numbers from 1 to 15 so that the um of two neighbors is a square number:
Solution:
8 1 15 10 6 3 13 12 4 5 11 14 2 7 9
(8+1) = 9
(1+15) = 16
(15+10) = 25
etc.
15 = n * Prime(n) = 3*Prime(3)
15 = 123 − 45 + 6 − 78 + 9
15 = 98 − 76 − 5 − 4 + 3 − 2 + 1
15 = 11 + 1 + 1 + 1 + 1
= 2 + 2 + 22/2
= 3 + 3 + 3 × 3
= 4 + 44/4
= 5 + 5 + 5
= 6 + 6 + 6 × 6/(6 + 6)
= 7 + 7 + 7/7
= 8 + 8 − 8/8
= 9 + (99 + 9)/(9 + 9)
Number k such that k^2 + 2 is prime (227)
Number k such that (16*10^k - 31)/3 is prime.
Number of Integer partitions of 15: 176
15 = Number of Partitions of 7
Magic Square Numbers 1 to 9 and Sum 15
| 8 | 1 | 6 |
| 3 | 5 | 7 |
| 4 | 9 | 2 |
Numbers of edges of regular polygon constructible with unmarked straightedge and compass.
Cake number, maximal number of pieces resulting from 4 planar cuts through a cube (or cake)
Number of intersection points of semicircles joining all pairs of 6 equally spaced points along a line
Semiprime (Product of 2 Primes)
Semiprime s such that s-/+2 are primes.
a(n) is the smallest semiprime such that difference between a(n) and next semiprime, b(n), is n, n = 6
15 cannot be written as a sum of 3 squares. (Integers that are not a sum of three squares)
Factors: 1, 3, 5, 15
Representations, Binary to Hexadecimal:
1111_2
120_3
33_4
30_5
23_6
21_7
17_8
16_9
14_11
13_12
12_13
11_14
10_15
f_16
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Undergraduate Texts in Mathematics
Graduate Studies in Mathematics
