Have you not read, "Jesus said unto them, Verily, verily, I say unto you, Before Abraham was, I am. (John 8:58 KJV)"?
Oh, but that's right, the book of John is not one of the "synoptic" accounts of the Gospel (singular, as there is only ONE Gospel).
Could it be that Matthew, Mark, and Luke's accounts of THE GOSPEL do not include "Jesus making such a . . . remark of himself", because of the way that each of the writers were portraying JESUS (Matthew>THE MESSIAH; Mark>THE PERFECT Servant; and Luke>THE Son of Man)?
But, again, to your statement,"none of the synoptic gospels show Jesus making such a blasphemous remark of himself", JESUS, so to speak, killed two birds with one stone (words backed up with action), because . . . in each of the Synoptic accounts JESUS did what ONLY GOD Can Do:
"And, behold, they brought to him a man sick, a paralytic, lying on a bed: and Jesus seeing their faith said unto the paralytic; Son, be of good cheer; your sins be forgiven you. (Matthew 9:2 KJ2000)"
When Jesus saw their faith, he said unto the paralytic, Son, your sins be forgiven you. (Mark 2:5 KJ2000)"
And when he saw their faith, he said unto him, Man, your sins are forgiven you. (Luke 5:20 KJ2000)"
And he said unto her, Your sins are forgiven. (Luke 7:48 KJ2000)"
When you do what ONLY GOD can do, its not necessary to make remarks about yourself . . . because others will do it for you!!!