, , . - , . , , , , - .
- , , , , , , , .
, , . 360, 360. 270 (90 3 = 270), , , 90 (360- 270 = 90). , - . , . .
, (, , ), , .
- - , .
, , , .
, . - , ( ) .
, :
1. 360; - , , 360.
2. , ; 360, 270 (90 3 = 270), 360 - 270 = 90.
3. , - ; , , .
, , .
. , , , 6 < 8 (. . 26).
, , , , , , , , .
- , .. , . .
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, - , , .
. - , , , .
- , .
1. , , 4, 20, .
. . , 1 . 2, 13, 5, 17- . , , . 1 , .
, 4, 20. : 6, 8, 9, 10, 12, 14, 15, 16, 18. : 6 = 3 + 3; 8 = 5 + 3; 9 = 7 + 2; 10 = 5+5 ( 7+3); 12 = 5+7; 14 = 11+3 ( 7+7); 15 = 13+2; 16=13 + 3 ( 11 + 5), 18 = 13 + 5 ( 11 + 7). , .
. . => . , () , , , . , ( ), , , , , . , , =$ .
3. , + 3 > 10, ≠7.
. , , , .. - 1. + 3 > 10. 7 + 3 > 10 10 > 10, . . , , , + 3 > 10, ≠ 7.
4. , 2 - , - .
. , , , .. : - . = 2n + 1, n Z0. 2 = (2n +1)2 = 4 n 2+4 n +1 = 2(2 n2 + 2) + 1 = 2k + 1, k = 2n2+2. . , . , , 2 - , .
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, , , .
, , ( ) , . , , , , , , . , , , - . . , .
, .
5. . , 2?
. . . 1,2,3,4 . : 23 - 14 = 2. , , 5, 6, 7, 8, : 6 7 -5 8 = 2. , 2 . , .
.
: n, n + 1, n + 2, n + 3. , (n + 1)(n + 2) n (n + 3). : (n +1)(n + 2) = n2 + 3n + 2; n(n+3) = n2 +3n.
, 2. .
. . , .
6. , 3, 2 + 2 3?
. . , 3, n2 + 2.
n = 1, 12 + 2 = 3, 3 = 3,
n = 2, 22 + 2 = 6, 6:3,
n = 3, 32 + 2= 18, 18:3.
, n 3, n2+ 2 3 . , . .
n 3, 3 1 2 , , n 3q + 1 (q Z0) 3q + 2 (q Z0).
n = 3q + 1, n2 + 2 = (3q + 1)2 + 2 = 9q2 + 6q + 3. 9q2 + 6q + 3 3, , 3 , .. n2+ 2.
n = 3q+2 , .. n2+ 2 3.
, n, 3, n2 + 2 3.
- . , 1. , 3 3 - , 3, , 3 1, , 3 2. , , 3, 2 , 3+1, - 3q+2. , 2 + 2 3.