85 = 92 + 22 = 72 + 62
85 = 1 + 2 + 3 + 4 × 5 + 6 × 7 + 8 + 9
85 = 9 + 8 + 7 × 6 + 5 × 4 + 3 + 2 + 1
85 = 0^8 + 1^9 + 2^6 − 3^7 + 4^5 + 5^4 + 6^2 + 7^0 + 8^3 + 9^1
\( 85^2 = 36^2 + 77^2 = 13^2 + 84^2\)
85 = 111 − (1 + 1) × (11 + 1 + 1)
= 2 × 2 × 22 − 2 − 2/2
= 3 + 3 × 33 + 3/3
= 4 + (4 − 4/4)4
= 5 × 5 + 55 + 5
= 66 + 6 + 6 + 6 + 6/6
= 77 + 7 + 7/7
= 88 + 8 − 88/8
= 9 × 9 + (9 + 9 + 9 + 9)/9
Moser-de Bruijn sequence: sums of distinct powers of 4
Numbers of edges of regular polygon constructible with unmarked straightedge and compass.
Jacobsthal number: a(n) = a(n-1) + 2*a(n-2), with a(0) = 0, a(1) = 1; also a(n) = nearest integer to 2^n/3. n = 8
Number of paths with 4 turns when light is reflected from 4 glass plates
Semiprime (Product of 2 Primes)
Factors: 1, 5, 17, 85
Representations, Binary to Hexadecimal:
1010101_2
10011_3
1111_4
320_5
221_6
151_7
125_8
104_9
78_11
71_12
67_13
61_14
5a_15
55_16
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Undergraduate Texts in Mathematics
Graduate Studies in Mathematics
