\( 84^8 = 1^8+2^8+3^8+5^8+7^8+9^8+10^8+11^8+12^8+13^8+14^8+15^8+16^8 +17^8+18^8+19^8+21^8+23^8+24^8+25^8+26^8+27^8+29^8+32^8+33^8+35^8 +37^8+38^8+39^8+41^8+42^8+43^8+45^8+46^8+47^8+48^8+49^8+51^8+52^8 +53^8+57^8+58^8+59^8+61^8+63^8+69^8+73^8 \)
84 = 1 × 2 + 3 + 4 × 5 + 6 × 7 + 8 + 9
84 = 9 + 8 + 7 × 6 + 5 × 4 + 3 + 2 × 1
84 = 0^6 − 1^8 − 2^4 − 3^9 + 4^7 + 5^5 + 6^3 + 7^2 + 8^0 + 9^1
84 = (11 − 1 − 1)(1+1) + 1 + 1 + 1
= 2 × (2 × 22 − 2)
= 3 + 3 × 33
= 4 + 4 × (4 × 4 + 4)
= 5 × 5 + 55 + 5 − 5/5
= 66 + 6 + 6 + 6
= 77 + 7
= 88 − 8 × 8/(8 + 8)
= 9 × 9 + (9 + 9 + 9)/9
84 = ( 2^3 + 10^3 ) / ( 2 + 10 )
a(n) = n*(n+8), n = 6
a(n) = 1^2 + 3^2 + 5^2 + 7^2 + ... + (2*n-1)^2 = n*(4*n^2 - 1)/3. n = 4
Moser-de Bruijn sequence: sums of distinct powers of 4
Number of knapsack partitions of 17
Factors: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
Representations, Binary to Hexadecimal:
1010100_2
10010_3
1110_4
314_5
220_6
150_7
124_8
103_9
77_11
70_12
66_13
60_14
59_15
54_16
<--- --->
Undergraduate Texts in Mathematics
Graduate Studies in Mathematics
