FAN OF TYPE 0, WHERE NJ = 2(AJ +A2J + 1) AND MJ = A2J(AJ + 1)2. BY T...

2- - BÁO CÁO TOÁN HỌC FANS AND BUNDLES IN THE GRAPH OF PAIRWISE SUMS AND PRODUCT POTX
Toán BÁO CÁO TOÁN HỌC FANS AND BUNDLES IN THE GRAPH OF PAIRWISE SUMS AND PRODUCT POTX
2-fan of type 0, where n

j

= 2(a

j

+a

2

j

+ 1) and m

j

= a

2

j

(a

j

+ 1)

2

. By the way, also c

j

isinvolved, namely k

j

0

= (c

j

−1)

2

/2, where k

0

j

(n

j

−k

0

j

) =m

j

. aProposition2.3. G

×

+

contains infinitely many 2-fans of type 1.Proof. By Theorem 2.1, n, n−1, n−2, m is a 2-fan of type 1 if and only if n = 2a

2

+ 1,8a

2

+ 1 is an integer. Now, 8a

2

+ 1 is odd, and thus, if 8a

2

+ 1m = a

2

(a

2

−1) and √is a square, then there is a t such that 8a

2

+ 1 = (2t+ 1)

2

. Consequently we get 8a

2

=4t

2

+ 4t= 4t(t+ 1), which impliesa

2

= t(t+ 1)