Among the statements :
(S 1 ) : 2023 2022 - 1999 2022 is divisible by 8.
(S 2 ) : 13(13) n - 11n- 13 is divisible by 144 for infinitely many n 
N
Text Solution
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Given,
(S 1 ) : (2023) 2022 -(1999) 2022 is divisible by 8
Now we know that (x - y) divides (x n - y n ) 
So, (2023 - 1999) divides (2023) 2022 - (1999) 2022 
24 divides (2023)
2022 - (1999) 2002
8 will divide (2023) 2022 - (1999) 2002 As 8 divides 24
Hence, (S 1 ) is correct Now solving,
(S 2 ) : 13(13)
n -11n -13 is divisible by 144 for n 
N
So using binomial theorem in (1 + 12) n we get,
13(l + 12) n -11n- 13
= 12 x 13n- 11n + 12 2 
= 145n + 144 
which is not divisible by 144
Hence, (S 2 ) is incorrect
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