\( 40^7 = 1^7+3^7+5^7+9^7+12^7+14^7+16^7+17^7+18^7+20^7+21^7+22^7+25^7+28^7+39^7 \)
40 = 123 + 4 + 5 + 6 + 7 + 8 + 9
40 = 98 − 7 − 65 − 4 − 3 + 21
40 = 0^0 + 1^8 − 2^7 − 3^9 + 4^5 + 5^6 + 6^1 + 7^4 + 8^2 + 9^3
40 = 2^2 + 6^2
40 = (1 + 1) × (1 + 1) × (11 − 1)
= 2 × (22 − 2)
= 3 + 3 + 33 + 3/3
= 44 − 4
= 5 × 5 + 5 + 5 + 5
= 6 × 6 + 6 − (6 + 6)/6
= 7 × 7 − 7 − (7 + 7)/7
= 8 × (8 + 8) − 88
= (9 × 9 × 9 − 9)/(9 + 9)
240 - 1 = 3 * 5 * 5 * 11 * 17 * 31 * 41 * 61681
1040 - 1 = 3 * 3 * 11 * 41 * 73 * 101 * 137 * 271 * 3541 * 9091 * 27961 * 1676321 * 5964848081
Number of ways to write 17 as an ordered sum of 4 nonprime numbers.
Abundant number : 12, 18, 20, 24, 30, 36, 40, 42, 48, 54, 56, 60, 66, 70, 72, 78, 80, 84, 88, 90, 96, 100, 102, 104, 108, 112, 114, 120, ... (sequence A005101 in the OEIS).
Number k such that (7*10^k + 71)/3 is prime.
Number k such that (16*10^k - 31)/3 is prime.
Number k such that 4^k + 13 is prime.
Numbers k such that k^2 divides 9^k - 1
Maximal number of pieces obtained by slicing a torus (or a bagel) with n cuts: (n^3 + 3*n^2 + 8*n)/6, n = 5
Numbers of edges of regular polygon (tetracontagon) constructible with unmarked straightedge and compass.
The ring of integers of the field Q(sqrt(-40)) has class number 2.
Factors: 1, 2, 4, 5, 8, 10, 20, 40
Forty
Representations, Binary to Hexadecimal:
101000_2
1111_3
220_4
130_5
104_6
55_7
50_8
44_9
37_11
34_12
31_13
2c_14
2a_15
28_16
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Undergraduate Texts in Mathematics
Graduate Studies in Mathematics
