An existential statement is a statement that announces the existence of a fact. To indicate an existential statement we use the words **there is** or **there are or there exists**. Some of the examples are:

- There is a number n such that n*n=441
- There exists 2 consecutive prime numbers

Let us solve some sums based on this.

- Express the statement 1234546789 is a multiple of 3 as an existential statement. Is it true?

To express any statement as an existential we use the words **there is** or **there are or there exists**. So the above statement can be expressed as:

There is a natural number x such that 123456789=3x.

By division process, we see that 123456789=3*41152263. So the statement is true.

2. What is the connection between the facts 3*3+4*4=5*5, 5*5+12*12=13*13, 7*7+24*24=25*25 and the statement there are numbers a,b,c such that a*a+b*b=c*c?

By solving the above equations, we see that 3*3+4*4=5*5, 5*5+12*12=13*13 and 7*7+24*24=25*25.

So, we can conclude that the facts are examples of the statement and the statement a*a+b*b=c*c stands true.

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