Math Olympiad (Primary Schools) 一筐鸡蛋

Math Online Tom Circle

One basket of eggs.
1粒1粒拿,正好拿完。
Remove 1 by 1, nothing left in basket.

2粒2粒拿,还剩1粒。
Remove 2 by 2, one left in basket.

3粒3粒拿,正好拿完。
Remove 3 by 3, nothing left in basket.

4粒4粒拿,还剩1粒。
Remove 4 by 4, one left in basket.

5粒5粒拿,还差1粒才能拿完。
Remove 5 by 5, short of one to complete.

6粒6粒拿,还剩3粒。
Remove 6 by 6, 3 left in basket.

7粒7粒拿,正好拿完。
Remove 7 by 7, nothing left in basket.

8粒8粒拿,还剩1粒。
Remove 8 by 8, one left in basket.

9粒9粒拿,正好拿完。
Remove 9 by 9, nothing left in basket.

请问筐里最少有几粒鸡蛋 ?
At least how many eggs are there in the basket?

[Hint] This is a Chinese Remainder Problem (韩信点兵“)

—— [Solution] —–

Let there be minimum X eggs in the basket.

Remove 1 by 1, nothing left in basket:
X = 0 mod (1) …[1]
=> trivial & useless !

Remove 2 by 2, one left in basket:
X =…

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