Hello, Dragon!

Let be the number of eggs.A peddler is taking eggs to the market to sell.

The eggs are in a cart that can hold 500 eggs.

If the eggs are removed fom the cart 2, 3, 4, 5 or 6 at a time,

. . one egg is always left over.

If the eggs are removed 7 at a time, no eggs are left over.

How many eggs are their in the cart?

The LCM of 2, 3, 4, 5 and 6 is .

. . Hence, (and any multiple of 60) is divisible by 2, 3, 4, 5 and 6.

To have a remainder of 1, must be of the form: .

. . for some positive integer .

That is:[1]

Since is divisible by

If you're familiar with Modulo Arithmetic: .

Reduce: .

Multiply by 2: .

Hence, is of the form: for some integer .

That is:[2]

Substitute[2]into[1]: .

Since , then

Therefore: .

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If you're not familiar with Modulo Arithmetic,

. . it can be solved with "ordinary" algebra.

It just takes longer.