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# If p is a positive integer less than 70, and 71^2 − 142p + p^2 is divi

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Re: If p is a positive integer less than 70, and 71^2 142p + p^2 is divi [#permalink]
Russ19 wrote:
If $$p$$ is a positive integer less than$$70$$, and $$71^2 − 142p + p^2$$ is divisible by $$49$$, what is the remainder when $$p$$ is divided by $$7$$?

A) 0
B) 1
C) 2
D) 4
E) 6

Solution:
• According to the question, $$p$$ is a positive integer less than $$70$$
• And $$71^2 − 142p + p^2=49k$$ where k is an integer
$$⇒(71-p)^2=49k$$
$$⇒71-p=7\sqrt{k}$$
$$⇒p=71-7\sqrt{k}$$
• Remainder when $$p$$ is divided by $$7=(\frac{71-7\sqrt{k}}{7})_r=(\frac{71}{7})_r-(\frac{7\sqrt{k}}{7})_r=1-0=1$$

Hence the right answer is Option B
Re: If p is a positive integer less than 70, and 71^2 142p + p^2 is divi [#permalink]
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