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Gaurav Seth 6 years, 9 months ago
Smallest odd prime number = 3
Smallest odd composite number = 9
H.C.F. of (3, 9) = 3
L.C.M. of (3, 9) = 9
As odd number p divides q².
⇒ p is a factor of q² or q²/p gives 0 as a remainder.
Now,
q² × q = q³, and p is a factor of q², hence it will also be a factor of q² × q.
⇒ p is a factor of q³
Therefore, p will divide q³ also.
In general, we can say that if p divides q² then it will also divide qⁿ, where n is a natural number (n ≥ 2).
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Gaurav Seth 6 years, 10 months ago
No, because the total fare (in Rs.) after each km is 15,(15+ 8), (15 + 2 x 8), (15+ 3 x 8),…= 15,23, 31, 39,…
Let t1 = 15,t2 = 23,t3 = 31 and t4 = 39
Now, t2 - t1 = 23 - 15 = 8
t3 - t2 = 31 - 23 = 8
t4 - t3 = 39 - 31 = 8
Since, all the successive terms of the given list have same difference i.e., common difference = 8
Hence, the total fare after each km form an AP.
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