Practical check the point is on the Curve [duplicate]

The curve I am using is secp256r1. Its formulae is

$$y^2 == x^3 + a\cdot x + b$$

$$a$$ = 0xffffffff00000001000000000000000000000000fffffffffffffffffffffffc (115792089210356248762697446949407573530086143415290314195533631308867097853948)

$$b$$ = 0x5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b (41058363725152142129326129780047268409114441015993725554835256314039467401291)

And I am checking the base point $$G$$:

$$G_x$$ = 0x6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296 (48439561293906451759052585252797914202762949526041747995844080717082404635286)

$$G_y$$ = 0x4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5 (36134250956749795798585127919587881956611106672985015071877198253568414405109)

Calculating left side $$y^2$$ gives me:

1305684092205373533040221077691077339148521389884908815529498583727542773586739078600732747106020956683600164371063053787771205051084393085089418365301881

Calculating right side $$x^3 + a\cdot x + b$$ gives:

113658155427813365024510503555061841058107074695539734801914243855899581676106121216742031186749037217068373713699401633275460693094202620308271598867055040123401752346577561684789671973397929725392419990583281258891711488349384075

Left and right sides are not equal.

What I am doing wrong in my calculations?

• Does this answer your question? Verify that a point belongs to secp256r1 Exactly the same reason. Commented Mar 29, 2022 at 19:17
• @kelalaka, yes if I performed mod with p on both sides and it goes equal. It works with base point and other constant points on the curve. But I got a problem with points calculated with scalar multiplication. I asked the question in another thread. Now digging in into my implementation of scalar multiplication operation to identify what is wrong. Commented Mar 30, 2022 at 3:27

$$y^2 \equiv x^3 + ax + b \pmod p$$
where $$p$$ is the characteristic of the field that P256 uses. When working in this field, we usually understand that we're in $$GF(p)$$ and not $$\mathbb{Z}$$ (and so we don't need to write out the modulus), however it is important that we realize that it's there.
When don't you reduce each side modulus $$p$$ and see if it then works.